😊出会いの泉😊

この質問の意味は文字列の素因数分解に相当するLyndon word に分解せよと解釈していいんでしょうか？
ならば1100個の長さの文字列は次の7個のものに分解される。

[[0, 1],

[0, 0, 1, 1, 0, 1, 1, 0, 1],

[0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1],

[0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1],

[0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1],

[0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1],

[0, 0, 1, 0, 0, 1, 1, 0, 1]]

どうもしっくり行かなかったので、もう一度考え直してみました。

A=010,B=011
と置くと
X=AB=010011,Y=BA=011010で
XX=010011010011
なのでXを3ビット左にずらすと
011010=Yが出現
即ち
0->010011,1->011010
という変更で並べる規則で行くと
0->010011->(010011)(011010)(010011)(010011)(011010)(011010)=010011011010010011010011011010011010
となり頭書の1100桁の文字列の最初の36個が出現する。
従って最初の216個の配列が
010011　011010　010011　010011　011010　011010
010011 ; X1
010011　011010　011010　010011　011010　010011
011010 ; Y1
010011　011010　010011　010011　011010　011010
010011 ; X1
010011　011010　010011　010011　011010　011010
010011 ; X1
010011__011010__011010__010011__011010__010011
011010 ; Y1
010011__011010__011010__010011__011010__010011
011010 ; Y1
これは
X1Y1X1X1Y1Y1(010011に対応)

同じく続く216個の様子
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010011010010011011010010011=Y1
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010010011010011011010011010=X1
X1Y1Y1X1Y1X1(011010に対応)

同じく続く216個の様子
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010010011010011011010011010=X1
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010011010010011011010010011=Y1
X1Y1X1X1Y1Y1(010011に対応)

同じく続く216個の様子
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010010011010011011010011010=X1
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010011010010011011010010011=Y1
X1Y1X1X1Y1Y1(010011に対応)

同じく続く216個の様子
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010011010010011011010010011=Y1
010011011010010011010011011010011010=X1
010011011010011010010011011010010011=Y1
010011011010010011010011011010011010=X1
X1Y1Y1X1Y1X1(011010に対応)

ここまでで216*5=1080個
残り20個が以下の配列
01001101101001001101
たぶん続きは0011011010011010となり
X1Y1Y1X1Y1X1(011010に対応)が現れるものと思われます。

このように兎に角0->010011,1->011010の変化を0からスタートさせ自己自身に繰り返し操作していって生み出されてた配列の様です。

GAI さん、御明察です。

下記の置換ルールを数回繰り返したものでした。

"項目","与えられた設定"
"変数","0,1"
"定数","なし"
"初期状態","0"
"置換規則","0→010011,　1→011010"

1906年、ノルウェーの数学者アクセル・トゥエ（Axel Thue）は、
下記のような置換を世に出しました。
(下記は L-system の書き方の真似をしていますので、定数も記述しています)

"項目","与えられた設定"
"変数","0,1"
"定数","なし"
"初期状態","0"
"置換規則","0→01,　1→10"

♥♥♥

アルファベットの「A」と「B」の2文字だけで、どこまでも続く長い文字列を作ると想像してください。ただし、ひとつだけルールがあります。
​【ルール】
どんなに短いものでも、まったく同じかたまりが3回連続して続く並び（例：XYZXYZXYZ）を作ってはならない。

​これを満たす文字列を、数学の世界では「キューブフリー・ワード（立方因子を含まない語）」と呼びます。「キューブ（立方体）」というのは、数学で X・X・X = X^3（同じものが3つ並ぶこと）を意味するからです。
​試しに、適当に文字を並べてみましょう。
​A B A B A B → AB が3回繰り返されていますね。これはルール違反（キューブ含む）です。
​では、A B B A A B B A はどうでしょう？
​A (1)
​B B (2 - これは2回だからセーフ)
​A A (セーフ)
​B B (セーフ)
では、3回連続する部分はありますか？ じっくり探してみてください。どこにもありません！

♥
先ほど紹介した
Thue が作った置換は
いかなる世代(置換により次世代を生成)でも
Cubefree word となっています。
♥

今回私がご紹介した下記の置換も、
どうやら Cubefree となっているようです。

項目","与えられた設定"
"変数","0,1"
"定数","なし"
"初期状態","0"
"置換規則","0→010011,　1→011010"

※ Thue による
"置換規則","0→01,　1→10"
をぐっと睨んで

"置換規則","0→??0??1,　1→??1??0"
と隙間をあけて
?? に 01 を当てはめたものが
今回私がご案内している
"置換規則","0→010011,　1→011010"
となります。

散歩中にこんなふうにしたらどうなるのかと思いついて
実際にやってみた、というわけです。

なお、管理人さんがまとめページで
繰り返しパターンのようにみえてそうでもない部分を
色付きで示していただきました。
有難う御座います。

※P.S. 私の置換における Cubefree word 性の証明には
すごく難しい定理を当てにしなければいけないようで
残念ですが割愛します

あっ。題意とは異なる分割の仕方があったのでこのスレッドは終了です。

任意の長方形は、対角線と、一方の頂点から対角線へ下ろした垂線によって、互いに相似な3個の直角三角形に分割できるからです。

あーーー

1×8=8かな?

ＧＡＩさん

大当たりです。
数列は永遠に続いてほしいものですが、
途中で終わってしまう数列もあるのですね。

巨大な数を適当に考えて同じことをすると、すぐに0になってしまいます。
どんな数だと（1桁になるまでに）長く続くか、またその連続に
上限があるのかということには興味があります。

(追記)
ちょっと調べたら、今のところわかっている最長は11回で
11回となる最小の値は277777788888899だそうです。

こんな挑戦ができるのですね。
そこで、では数字の方式を10進法から11進法へ変えてみて挑戦したらとみると
[6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10]
=78651871429395862061789067874710687825489797403089215(十進表示)
が13回続けられる。
更に
13進法なら
[7,7,7,7,7,7,9,10,10,10,10,10,10,10,10,10,11,12,12,12,12,12,12]
=24356446321678355215229300(十進表示)
が14回続けていけるようです。

他の素数での進法も調べてみましたが 29進法で
[5,22,22,22,22,22,22,26,28]
=2894282817967(十進表示)
で18回(なお調査範囲をもっと広げれば記録更新があるかも？)
このように少しルールを変えてやれば持続数は増やせて行きそうですが、限界も当然
起こりそうでもあります。( なにせ0が入ってくればすぐにストップですから)
なお97進法では可能な限りの範囲広げての計算では連続31回のものを見つけました。
以下がその数と経過になります。
元の数N=
[35,
70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70,
75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75,
96, 96, 96, 96, 96, 96, 96](九十七進法表示)
=880081036693018055569997022690825077554547958845112225633353085723385569682192201612460614697(十進法)

その後の経過
1;[2, 8, 81, 93, 74, 10, 20, 52, 88, 20, 46, 74, 38, 39, 39, 38, 94, 61, 51, 84, 11, 19, 13, 47, 80, 96, 52, 54, 3, 94, 64, 46, 32, 40, 96, 57, 42, 6, 22, 86, 9, 3, 13, 29, 86],
2;[5, 62, 51, 12, 8, 59, 62, 67, 26, 27, 3, 87, 83, 37, 75, 26, 41, 62, 29, 6, 66, 90, 45, 31, 49, 60, 44, 17, 52, 89, 26, 3, 29, 33, 74],
3;[18, 54, 85, 93, 74, 52, 85, 62, 93, 64, 84, 27, 58, 93, 79, 20, 72, 35, 55, 26, 29, 79, 21, 50, 3, 16, 13],
4;[1, 86, 80, 51, 71, 39, 45, 2, 5, 67, 35, 54, 77, 49, 14, 21, 15, 43, 84, 39, 57, 28, 93],
5;[3, 22, 55, 41, 79, 66, 47, 1, 62, 6, 61, 75, 85, 43, 14, 39, 75, 90],
6;[12, 41, 7, 87, 7, 59, 43, 16, 55, 28, 95, 68, 96, 58],
7;[63, 92, 35, 93, 94, 73, 84, 56, 66, 70, 42],
8;[1, 58, 41, 96, 49, 13, 68, 79, 72, 42, 57],
9;[17, 17, 51, 35, 64, 41, 64, 1, 94],
10;[9, 75, 29, 77, 47, 54, 93],
11;[41, 41, 62, 96, 75, 27],
12;[2, 34, 83, 34, 92, 43],
13;[8, 55, 75, 37, 49],
14;[65, 53, 67, 79],
15;[19, 94, 94, 34],
16;[6, 24, 63, 91],
17;[87, 71, 82],
18;[53, 80, 77],
19;[34, 67, 75],
20;[18, 15, 33],
21;[91, 83],
22;[77, 84],
23;[66, 66],
24;[44, 88],
25;[39, 89],
26;[35, 76],
27;[27, 41],
28;[11, 40],
29;[4, 52],
30;[2, 14],
31;[28]

12391は、先程(x,y,z,w)=(8456197,681359,9262933,429569)が
最小解であることが確定しました。
これで「???」の残り4個の9562,15427,18311,19219を除き
他の最小解(max(x,y,z,w)が最小)(n≦20077)がすべて確定しました。
現在「式の値(=x^4+ny^4)が最小」である最小解を調べて
いるところなので、上記4個以外の最小解が確定したら
まとめて公表する予定です。

(追記)
9562は、今しがた
9868696^4 + 9562 * 410163^4 = 9938304^4 + 9562 * 65587^4
を発見しましたので、これが最小解であることを確認すれば確定です。
(確認には数日かかります)

らすかるさん

こちらも、20001<=h<=20077の範囲の小さい整数解は、"dqde4.c"によって既に計算済みです。
今、h=20078のときは、max{x,y,z,w}<=2000000では整数解が見つからなくて、現在、max{x,y,z,w}<=3000000で計算中です。とりあえず、h<=20100まで計算してみようと思っています。

もし、らすかるさんが、h>20000の範囲で、整数解を見つけることができなかったhがあれば、楕円曲線の有理点を使って、整数解を探してみるので、ぜひ、教えてください。

20100までは計算しました(除20078)。
20078は並行してゆっくり(∵他の探索を優先するため)探索中ですが、
5700000までにはなさそうでした。
※バグで見逃がしている可能性もありますので、引き続き計算して頂けるとありがたいです。
20100でやめたのは、20111で若干面倒なことがあるためです。
このことは後で書くつもりだったのですが、せっかくですので今書きます。

「面倒なこと」というのは「0を含めるかどうかの問題」です。
私は1≦x＜z, 1≦w＜yで計算していましたが(0は後で計算しても簡単なので)、
Seiji Tomita氏の計算結果には0が含まれているものが79個含まれていますよね。
しかしきちんと計算すると、0が含まれるものは195個になるはずです。
（うち11個は4乗数で最初から除外されていますので、実際は184個です）
どうも、2～5000は0を含めて計算していて、それ以上はほぼ0を含めずに
計算されているようです(5335,12595,12935の3個だけ0を含んでいます)。
というわけで、計算結果は(いずれも20100までで)
(1)「1≦x＜z,1≦w＜yでmax(x,y,z,w)=max(y,z)が最小である解」（複数ある場合はx^4+ny^4が最小のものを採用）
(2)「1≦x＜z,1≦w＜yでx^4+ny^4=z^4+nw^4が最小である解」（複数ある場合はmax(y,z)が最小のものを採用）
(3)「0≦x＜z,0≦w＜yでmax(x,y,z,w)=max(y,z)が最小である解」（複数ある場合はx^4+ny^4が最小のものを採用）
(4)「0≦x＜z,0≦w＜yでx^4+ny^4=z^4+nw^4が最小である解」（複数ある場合はmax(y,z)が最小のものを採用）
の4通りの表を別々に出そうと思っています。

20111の場合は
(1)(2)では (x,y,z,w)=(54,12,107,11)
(3)(4)では (x,y,z,w)=(5,1,12,0)
になると思います。

他の例では
84の場合は
(1)では (x,y,z,w)=(13,11,29,9) (13^4+84*11^4=1258405)
(2)(3)は(1)と同じ
(4)では (x,y,z,w)=(17,10,31,0) (17^4+84*10^4=923521)
260の場合は
(1)では (x,y,z,w)=(236,151,536,121) (236^4+260*151^4=138272300676)
(2)では (x,y,z,w)=(126,141,566,35) (126^4+260*141^4=103018129236)
(3)では (x,y,z,w)=(7,2,9,0) (7^4+260*2^4=6561)
(4)は(3)と同じ
のようになります。

現在、9562,15427,18311,19219について全力で探索中、
20078は「ゆっくり」探索中
(1)→(2)の変更点も「ゆっくり」探索中
なのですが、(1)→(2)の変更点が出揃った時点で
(15427,18311,19219,20078の解が見つかっていなくても暫定版として)公表する予定です。

らすかるさん

注意すべき情報を提供いただき、ありがとうございます。

最小値□と最小値〇の違いは認識しましたが、Seiji Tomitaの表に、0の扱いで、そのように微妙な仕様(条件)の差が含まれているとは全く気づいていませんでした。

もともとの目標は、Seiji Tomitaの表で、???付きの暫定最小解を参考にして、真の最小解を求めようということだったので、少なくとも、楕円曲線の有理点を使って求めた整数解では、0を含む整数解は除いて(実質的には除かれて)います。

そこ(0の扱いと更新データのまとめ)は、らすかるさんに全権委任します。
らすかるさんの貢献度が圧倒的に大きいので、Seiji Tomita氏への最終報告は、らすかるさんからしていただくのが妥当だと思います。

h=20078のき、 max{x,y,z,w}<=3000000の範囲では、自明でない整数解は見つからないことが確認できました。

-bash-3.1$ time ./dqde4 20078 -m 3000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20078, N = 3000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 150901824
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...

Found 0 solutions.
Search finished successfully.

real 425m0.549s
user 424m46.821s
sys 0m13.369s

x^4+12391*y^4=z^4+12391*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか求めた。

718901034532286548723430458587047903777397151289239^4+12391*57451008357573276494993444645137467164876367078809^4=727061994739772229807032044735698076441939872261067^4+12391*56090848322992329647726513620362438387452580250171^4

108507614053875066581083493712865633588461755190996343969269992471395^4+12391*133293342027510367029707317699590327283678432380364538379760440212518^4=1366728374859625343076619603953901090348685131819110157497526007643823^4+12391*76410118106781345719548700673915582176358797057654430541615562316220^4

1411625406536963531039295242821235124570647918283769376516744024055405341729039751277217310778107^4+12391*821755213999580265894610795269375518179995503951438151227966443982501329922251102622005451153374^4=8578366234005402994696689513856698823995566655446340998771949100918482581479281230516287141036263^4+12391*372701590578492978048288249903201765057490952242323785814567735494678210036122477251172853889652^4

156256736172629294620718121293199569268388106111239903656479836534361231719816052997347706369482462611479479978867602908124643459422544438157367^4+12391*96000392843172828828056377093941687935667216833527089953012451806485158061320169106476477610106854092841122218015239685309435898843416557669578^4=1000823887766598033540929425648619669485246495307590087491155694930086502788250452727183840171158698525117713245512339885865994051471756872780371^4+12391*44760799089155294325312173631961662100475848032531274019433524592802387116752230848496211356839185226098583326425549810980789199831452181434256^4

2062618299573624232658125245931015178923662518713948160344452257439223673293298204867901732057353473700815584907901282375010793680585041140446165305009632051261163527263302114218919418056065869733168979732^4+12391*350317150619006443840590502313762078485205050933902626332517037230861457672760653994117521390785336993634026115619624464578430975583077821316570775583871832495365017906968709917263966965975555397100492151^4=2133746002232724025069100838931024232135874457434982630109194080922316674826476060466454598760390085942795192540961136927633610183491976674785193879595558248310794794134539308878551962511822393414758061056^4+12391*349076899682051599113947178496577823358051111757585838743090685829395267013868390228275200412171922946967770125857445419195636335096425147888655755183659884099961368992671527265647929795339155127554014647^4

289914283469733560115164798311638199604763182604163874105488246336603646746184040071350777878201176306979497164282835044557927893465784911964966865450575242073432120859040017778849825965811424502017141129698966709447831652199^4+12391*401509801702304538187848500651738992694851062707385540404367881860408145124919014910167226454322233307845996560958069641767103703035864469219870531320728913560811895172620294689259745616965647427829353168841723780259106370114^4=4106852152108904135714832702427422169676331402910278590132247816522293965205735203255188100423543029118313524515919531245538675094531881355580718737137928447628967071400138306979330539870318217477475543676102854142016717017219^4+12391*234646509737557224412096150034225002317076974010300245600092046503873574618339512287138993969901408827376341330981379725063020830475151604716088113960496620698443929917562753510820373367118818068080380588892257458502374524056^4

16234335126153905708410689831063421604403951305063445916514157281460011455770450773977433977444982795487653051355292362630133832365381986822344369661900424218931124117270939644832561028338051203512889774174902395042851819020492286714900705152874979732514902370924484153237693074067^4+12391*1730136839304938321396159962200371805581510458359327099393687616086911230467606821708596600894616229503601469174502003223875492552961762620304255839391859366128586499506169639223000478735245624248622650540594754794752333269172657885184241148048170560398155446362844991722968481495^4=20101674015145462955403683949785781293548242224305187933177072515079071559365558715923031337761922080173217527493486573529112092824258180436183896846552690419435474526976167627687846208007793627036074363313279631334158922880237765433847251260783694670095303217490801469261071081455^4+12391*1085580357806345446897327609079978524057461971819036763283201743817067879868422164717663707508459682056007389818136301407379115809815730351331001308616481666044528097888631642080452948790288553661425219017531882079534482625881744765359816796730051404134755305268458772385738813597^4

15874375355783090673656668327163242130253209346987708696186243275442427769808265260424939088299695508597698341092854544314945893412528273119328585429643068419120131314098633198398306975885370330760769870926271987995387319938268965729193075520014110369361106349765436811246300439952714^4+12391*3240987771633554020647641323061665755078769543272630672206517428897510064782816946990587723643782493291881864469005507040360001099270388252902262816375486251313015545135980986726570418434082832105940458221769133120253604833047340095334589232520645330848674838783165326225907530754929^4=22323906240307374289317521344634347161084862910209572160032884397559229498463831451745074530941449873797380116755319198420221970719837990356513180023555382082914154439852981912861836753667970686057299442580477627764406902808927934984710463512442694693297835264773209900462337965736322^4+12391*3125392494381523473181390288904599126810909166260249470496670516602766146595865838371081212896408403773964545172356783415501309589457322326404698092490922165692698747189288198483453536491474004030404427362689136173045432291485476690316000606222155512927815430306609125725532203526577^4

....

x^4+12391*y^4=z^4+12391*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか求めた。

15277093978728943657393459790075249923568307887584693592060174899^4+12391*42527056178166824551284793142174230391964672746991926700536552233^4=83937521680192742075382630376335051786006171700146437781864812839^4+12391*42514042958051763219666141286177456787670595471063328762827722971^4

376484714376979186210390059659642860967045881713612982236369451420937035241448148^4+12391*28600962290902148156345722270872502802283396156512900371958514587954160438326715^4=410449945157849496180525916560727648839520008975540387792717012878975656143700250^4+12391*512092664129546103770726501485886802694427210853447247767966661793228906460801^4

542874408321974323871704267311992273796610208392043725379419014669450299570886669193786070771806128785693805332083989843914881796018^4+12391*39791112837135676027707328533656587061509718819455634476531926595817147331525209603179227899105889677801294831057283046589319703789^4=585996826958479019168074728380216706238658714482694247547222103605108430398269440037379930865335483880863249236073510412528556931744^4+12391*2829039720131651487961219046607073539753856456040901189843564650967320908054263165813062104652156739084628627637693987777598158881^4

3007920550737575989990662218263835033944846837515637993458765059315965607343753587087770843961563329430225298501545445823603835797822374851558800278365870994138^4+12391*235865131269969224402549844781168820308319628532157627063639524186673271932371285659468722244392310218502910165789003805888723889168934081725688675351148841671^4=3311158792670584544992519679637933733006431712318937879658397211318681953785709564101104692360017018749452934694039746598325838076797186105628422819294365542916^4+12391*24053361815466679884756550682344350315895978442099418250330891815655025017876694637674576382853709197977920856348968286730135207095189850333987788301846485853^4

7764521586482365018237805467084666904658961489309140761264069313930265713087031676220708041151228418587062075821562267576858464242486211580767958786074890864958694407386196265088986613109283859530365620228866406772077581823244119003579903010183468050011981689^4+12391*17338404547108543116259119985229282533991830019400951758286605386517705910151398249316264691042372980188713121177665797572388612110968864560562004081496189904187410030309122524940139065715507858716821475287232061544368963715735419303875163569125302497038729544^4=48196403647529978436230096139075397122574229134702839837261260978245856464607736285622356310605005021090288991607673717813656252868033689231599508367286414923346312185516339579411169675910736045116194215328655793955852937002587650426202575948631549037383043143^4+12391*17317494362360839813448557733619914795649827962365076021139558897181371876866348558742290968489435536242624235210429731202009492425214687711579324130970830717287690922373857458764589273828594014642460177655444556041724197866559036201229984663830195492136465988^4

197005198877891792415295739138889224084301770892109910419346146605534109979729674190574836574549099852299573677215107070473602245134134166303584861708951764566871688516785445227550752347604039283427542445974237376482843396934083966121299800992069459337187199989493817086789850346234483215779720460679764500547272^4+12391*13857293398254154630691800551860763751034702199063046446437023596770830279401301523240880349242507562533060559217944911438937709907148775127326066209260546653196919242182930348793549775211869366338410164881308474730709472260144640327639184981597578927757859831726238847198200819113549371421319784280460395700921^4=210485242426108336762350859388250289878784439927634863236752128925939801405089075660650450982409512160351661774047532939288066603971593291435867368692658426758127391722109379300455053606350177799825309768394396829075513475566367574244527154420708172449729767878598328252678279806645944718398610555789518099097002^4+12391*2302970356925688047501697480979850212906700168613086888660467322137380486236100263176067999647868441345556476218722738169396830903612382156798203080369121917834887923333844000589862982000893495140323888521171801079849404861044404793444310614192967688435658783922372133579546995903725226319413988472100168372581^4

64871946524374857798436978719426690202944881997088490691539997954711485372750582099917293901961332354294271783463359602989292786878890981819259792719212870938960470332293184668393621170932020126500426852370726627575136752952393090515165122069627736027673146418459215488217739184100822236317171785301109823775979661776311843546037^4+12391*6592451303082184285953064436740695091205409766142682674452926449184082693323221812902767144909467219866606550634746104114416582993560132180354972816133948327165630025336086545934085136664749402083552568103756976485440548188903310568032400409755897983420981080795511641507046801216780820584744269323988924480623053993510732897495^4=77701576021075672975958106417082771445131219685753772901870598537107549237586221424525179720014536257465796644307511838503257595917093161708579915911833338087330071684771141098330922196080447044053415238151517399859483401450480146120808315676543993224634901806106490961953336992494025421322588482782376976204853324364684900989895^4+12391*4404373979804228723350759304107374544954308252713273505830445478583972047964469036761134984850421839994700472945955812040410396182041736296205132777540737800008313991073590394012172884891045098676151762565492256901142293380885594236804622681886608185403380680045010193123465605977393337991327185659954349029840085367951887768669^4

80118384150939624083310811114753197072348241374442335256638309243532634511547361103685872007432904672420200547314982108619487768282142576499332840711725544766004055431730683585911674418259830984229670768270143390847951346915308603593849765591244815048510344079889699852747155207202043173004446000834372278362275528444712948245059907463682027313789639388192741408529^4+12391*8540117553011406471796659139346120813664883059925735511091423536029981230580661399756278473243468774571061737740929132090801814133739980507476662774527503600452132910183263665059155157769358399571779360920755283263991054262628887479587286262931424669885204228371696882579799656860751559188202553263608177464998081312993980615522937710731753175026022459281548773388^4=97250804328017714828442099406467479328044145874483229259581288011528826034703393658768631788210017526374658457669631400476780893951307747663296700422535459524847799327490441987452209080278207537117160607724168615573362942440622366660152009164770228794153055074453634694851990636938918317927964127457324190756174268283434740018079650838512376809917805317459909281583^4+12391*6144814027341242738315873682123263976931606511537887920002558265109611503553080790314658481708342243104187899705913118072592293582687309061635216977595280478556790429039386393404160266817821502903211930039837766500647456187640052291528922514376072826379976624111675839224344997199427136460527269556064890301200838548767555189922556610551403535940976908661737974944^4

....

Y.K.さん

(A,B,C,D)=(110135,249568,244580,325193)は、
　　2*A^4+B^4+C^4=D^4
の整数解になっていません。

2*110135^4+249568^4+244580^4=7751937824733931778626
325193^4=11183165553400911588001
なので、左辺と右辺は一致しません。

(1)方程式または数値の間違いではないですか？
　　しかし、
　　 110135^4+249568^4+2*244580^4=11183165553400911588001
なので、 A^4+B^4+2*C^4=D^4の自明でない整数解にはなっています。
(2)Y.K.さんの成果ではないのであれば、だれの成果なのですか？
　　どこかに公開されているのであれば、そこに整数解を求めた方法も書いてあるのではないでしょうか？
(3)解いた人が誰なのかが分かっているのであれば、解いた人に聞くのが早いのではないしょうか？

もし解けるのであれば、解き方を教えて欲しいくらいです。

(1) すみません... AとCが逆でした... 2*A^4+B^4+C^4=D^4とするならば(244580,249568,110135,325193)ですね
(2) これはEugene Goというmathoverflowの方の結果で、下記URLの質問の回答としてA^4+B^4+C^4+D^4=E^4の整数解のリストをあげていらっしゃいます。
mathoverflowでのEugene Go氏の回答：
https://math.stackexchange.com/questions/5145111/in-order-to-parameterize-more-numerical-solutions-are-requested-for-the-a4b/5145556#5145556
Eugene Go氏の整数解のリスト：
https://drive.google.com/file/d/1lEEdTOVH_7V-dHQl1PjqPx5Emw8K4qm5/view

しかしここに書かれているのはあくまでA^4+B^4+C^4+D^4=E^4の整数解をブルートフォースで求める方法であって、A^4+B^4+2*C^4=D^4の整数解を求めることに特化しているわけではないのです。しかしたまたまこのリストに入るぐらいの小さい解が載っていたので、A^4+B^4+2*C^4=D^4の整数解を得られたというわけです。

色々と工夫していますがEugene Go氏の環境が素晴らしいのか私の実装が下手くそなのか、私はまだ最小解(244580,249568,110135,325193)すら探索によってでは見つけられていません...

(3) 解説のpdfがあるのでそれを読んでいました... けどA^4+B^4+2*C^4=D^4用の最適化の方法が分からず試行錯誤中です

Y.K.さん

Seiji Tomitaが以下のURLで紹介している
2. a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4 has infinetly many solutions
の証明がヒントになるのではないでしょうか？

http://www.maroon.dti.ne.jp/fermat/dioph63e.html

参照しているMaddenの論文は、
Jacobi, Lee W., Madden, Daniel J., "On a^4 + b^4 + c^4 + d^4 = ( a + b + c + d )^4". American Mathematical Monthly. 115 (3), p220–236.
のようです。

・Aは10の倍数
・Bは5の倍数
・Cは、Bが10で割り切れるとき5で割り切れない奇数、割り切れないとき5で割り切れない偶数
・Dは5で割り切れない奇数
（もちろんBとCは交換可）
というところまで絞って、何とか最小解までは探索でたどり着けました。
しかし2番目はD＞1000万とわかっていますので、（私には）かなり厳しいです。

Y.K.さん、らすかるさん

2*A^4+B^4+C^4=D^4の2番目以降の整数解について、ブルートフォースでの探索は困難との結論が出ていましたが、非常に興味深い外部の知見を見つけました。

Xにて、かいもちゐ氏（@Kaimochi_920）という方が、まさにこの方程式が無限に解を持つことの証明と、それに伴う具体的な巨大整数解（50桁規模）を提示されているのを確認しました。 投稿メッセージと整数解の桁数から見ても、本方程式が楕円曲線へと帰着されたことは明らかです。

該当ポストのURL： https://x.com/Kaimochi_920/status/2093769056121999782 

ご参考までに。

かいもちゐ氏（@Kaiえいmochi_920）のX投稿
　　　　https://x.com/Kaimochi_920/status/2093926485098660240
には、楕円曲線の式と元のA^4+B^4+2*C^4=D^4の整数解との関係が書いてあったので、それを使って、さらに巨大な３番目、４番目、5番目、6番目の整数解を計算しました。

[A,B,C,D]=

[49494256269168883921893536501755051556767975295914677935284954387412484692879666198489957014418420251879785591236298119337198884489585465, 93764198766252763890432809404866529374544191829088062449961647867739247626037659251559888322722610863702742076798967503976470276124891552, 87651612318971616899430892021752796370990837975548428503301481603367277690574374614094885746471525222135789942762282336062876847882686900, 119120345356566624443103411153397529190918659231499392470804555719384197453210796755123761028125283297778707622699668720872038417957894073],

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....

2*A^4+B^4+C^4=D^4の整数解については、MathOverflowでも議論されていて、Eugene Go氏の整数解とは別の整数解が、Vepir氏やAnders Høyer Berg氏によって発見されています。

https://mathoverflow.net/questions/515812/more-small-solutions-to-a-new-infinite-family-2a4c4d4-e4

これらの方法を参考にすれば、さらに別の整数解を見つけることもできそうです。

x^4+18311*y^4=z^4+18311*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか見つけました。

2058516257115494225881989418107119989469227899743716782847778435868813395798021389653635966043342526411045763736^4+18311*140816563264797664543165686455568105100816729257441107392998881857135335712200255180610547352933151591708179239^4=2239485634325116509795768123392077593482761626918563673845608507127848848546217577933295627208853908361797075674^4+18311*20170311791716141933979882932263035758460911140876513394445501017778367213402796327504106575925563624540637947^4

161695921263337790762396768802689480717103295095507313777382268628824069853098865957870902817582794589176090513891917759150172047825380221764746136144271643877993432648719387740618680810489825352729258103765311843020344985918434609620295431478977205916192372941346084701009581077039315284763409163031225277882404504257140928941099897662716342827568771794507172529837154064894601439273536090286397502679545498844977372810155938391758748088233835618949^4+18311*19845802461189151015513084540871482718329809172298360522065925231532458386078843974549489116439959560701220805362472965789143011307857188750157519516195568016286208414226012256463410411496481579571596769576393270601253441156493175952550481899282786604674830011524105315488065020471568387894080910826790085655436781044781946484778074552557307825148321461703953649555692628132948487051048599323165713589862177984405553668411892083367280271761055339773^4=216142673387597074462953327671256283529091259160308065155760534572154016021304114990626676791042225560906167990244330490581429446174447861425305601576835547964607295055709339067186031723316896127294869590940212681755442471499659246184478037518575386305771502130068444945322889982022173227440144018464566042416205385573905243826339872851341610101716560997304057016666254707269541826241215280589396816315586455190811906456187221790649406031885771505447^4+18311*16452032288317038118191288038173052489662166870902140396852918730687505726057988713954360199199661087118830845539135521831695254258187904356882124105513701374789699857100621961248156863721565603472144221873540621888811549230989915090237922127116000321711256114290801514054140916183670240557075659462103757367097139833060930105381908906526203690950204673493969341663707800117011770927404194212167162167498459579484135428942296849226491690673568584559^4

209106284056811223469403015630853341440260835503630932030545119191403679751909684797129340912084184614485914499720958138494142698137415979795495562123094075896654999823438014732476861764841374375795486647490199995953860115526184815051222068644149494919635888717466750686100542146071462467903038737066222728615832938766088870251203613356768456744182126897134782367625825844123014766103810561387297161366550457161601775477576968582862961026003977652811998084559645924014078054758188534580878411980081269449805290069297076532213639706150672261901335246505690901160006828080307762530679115993065568911378196464415117543435352028034427100411066381703222702347471104160258528110166741064789277994006952255771096827279600317353041686081440441430835923638087368261710074370707872538290245174538179039869232159611844332031504710263915773983501851440168109295485358352373872076245141856458953065442979935305402088114872405848438508986512859891218524272075359176149525695630113491062337790453645469858532227728852269522^4+18311*22016122299032078861425577370359809808518197315197109116574572907013996062659477133723832766605629752215710448653585690779186262215425198234895829159279526948513556236649573496439421703090093434375605613689147005568521824787961164176963878368142799593935478837578560070552219799545086023646933549854478730412724369894759303032684600894004406276767737245113873089435898896748380888521205203853898120293717841513353610623599133688835786510441025970913744551141265220371352755728578221167393504119235976885977935422511399756284741150488375782092390743765066160716961361919648847201763855994435373433366744175235290454808492111581887436822386464506932409139300122636917147051672407178904082198168827352038118564894271617390051137926562629211023049363872102377813397529468341304710211222134132605878509082167707568555027765725553134816857895065953468231458272486315403554034592790127096305945700486609816714945257360450505074579329402994175291701801710146122541119788662364399098250761661836559745012886428470077^4=266122085724986442555294986855474484387937757877930707499168995149996261864850220874629845712707555415743422268278478328428035401478336919382314358642815300188486913062326665146977401858424400345023027653258931394345239810268265820092368404781289328069991655059045975769327796364229845952759448969094049308174488095615938959786838867286502958432266808787119204392757727355346008200202658899626219626113175498710988590809211681598807788286208139776947487532425539898887068703146542930359176648003024171694085713335426858656485503791470304689960407887837575972002684910551227710059685958696005885987331767847287626584346121086363826269753464346654273173889046428399726857940794580287831128935339044594476161659628407974320970989214334330479204333536667418934247565711682074184579577318342765131976286593830513853783329055108284377057794359042894916623599590778347705928360891253048805111360965624065248704760265163872733440689456962140468746567929007495806604927443382670392154887258588762743798021448749238404^4+18311*15994412146418067195835736779387618823266417601002741195841344398714392012634213584609837100476617448622628063718094435843408873345188761489650035187201289246041052589276193446560938359298590545109421723490007260025731305040092839183800345723283755839635032056807589984932616345893836299590673271497405655959712401338474089991072235059151928181955384014875741593985368777400281400878027021638716856204032186186237599597490674988460764996361748778509915080769330762877307676530324709351471986562725957943542346754908454993229834906391379169946991017122857219844824026394297784484240705807524837950602303413346382239132020593971045342739212178793767905221750093522728406168746152303123818429385900873765257990004933487255235064162033296821222557235181264737211596697847793126149343540402258122192860540644738779279521797504025933899337110002531069987284549131000485680709240140932805057999623305896747696151671144899024879889299998505324856495434055400315511701420183755154113147108300358697098849593502842511^4

....

x^4+18311*y^4=z^4+18311*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか見つけた。

326646532263012904^4+18311*114702051298947271^4=696313211630008382^4+18311*112622336232835237^4

53194817657909603141924483163009761569312681243087128335374311482090011^4+18311*43729171208544681761515438580790369672494225775442469461224543103035425^4=330903342897730847670496434836982250471986013170858861765613657624221215^4+18311*41625975581597640641244765419207855225572150760989972783439450031700403^4

1351009240186291281970681912779364066848507058305364851688032464243166461602^4+18311*132627078050100353913610273824584294530051837114714413230326478309024302159^4=1726748828724426959752057867854260003069104823444521954321548623437340844628^4+18311*49129391708292425517748950474607419814363444861568390422878442932541105931^4

2237815468546911294205853436988208096069387773140352043318055977334757235251540261137^4+18311*164537947952016187861975061988687516058308092947714342016182076593853166138829235392^4=2414598817227468925489757900581238760954228233126304775345162604044076424238368011439^4+18311*125252759356336714243329625634680701639454657395280401565713937325115568586200846436^4

5498123119700252827860894662808774794947364970154866005151597328745257903149834702895029877962155169251^4+18311*673285868660234518816048992837763457633368462699552884680311370149492632065572392908870452918916860519^4=8269476976700176868908397730828002561833266193286757805197777200335773811775653755418750369287931567673^4+18311*57429455993584731916603866611268398325390413114688040225604732018266874593168159014710343735410994203^4

77815390249571646530710743471522531683444052731068978253671410602316222550201505835644995589408017080375727279134458125959709850^4+18311*5944769631178983611794547063313414286434393859304248118465301229190697268170015544501209384374503618040168479379076632902864583^4=85650918380428763366127468463269649797262188312504334141656416450269863441231559647742245097545834168158220348812815775021068796^4+18311*4203541157655179870590830398480721372252585952318613476690855485200999292385559141812931715899433154088503352783886044222562595^4

140046087260029679041109011539639634249477385428145848564192761954141925098712363141085436428368604964877888095562558515023446887887308814283324900986279581206^4+18311*381240467987590416233916409671242669749001842359483184471174575537137516646216652320973644329821353420052359048813445914783568066129562752085489773999636071733^4=3398974836579626093543493595979609757439668044440539259404136660739851213243473798483341966468335709146376383644563693497962476839285791065219154256118742457116^4+18311*342965920750097675877724609093195135404373859643270906826590735304131214052619222199527806790171336398058417739853472970313994145292322192566916749363133456247^4

73116878683820012107428975918052451857911609989175457709774064796511832365717705554986278746210721154420379435587159583360444145135330122904161736131193391985926840^4+18311*10770637252895355038421879181081388888849350792131693777294408531063511040073574029137982429015247677494325970556834805289597161738799395213783740536803579841640011^4=128761784151657099092500279168436377948489048734514677558494608017447483229114170624059985463961985939522527030761963947726576098757468418387586379183235435889270982^4+18311*1594897295512886513816188207892816909056746706832577300199045518033300262903418208433952397151700052528373495037566164569543272399453559338088402363650207692436465^4

16936873003931606403481823804616926664499038751533146769445925895687884757337562056092989822561981246867153697052351895432162076701582763357259538275383393518811067201049527397367452499004679890606232346453349^4+18311*1710740122915340503275287408215648190110732402587405562575196452292865485092671269618420821763793556998020114828344697739266124658589859963219735334354573296588487561946102422831880695424468383884038430506877^4=22068473911183295890768288524990204824253768936335438486419564150784507988704829308789333473751968343084072125574438239945219124244248806111868840073187846554433864626265494704963762847114094594888611878980879^4+18311*570384365748298394989406359243808599054125694853562958803276840049171433677722991241455565943796424505371575156769954514142336315775183795528779379286917066450088134120331910032700618066820671821287423278537^4

6399480080965242395457273971023615143416880709604723406170122519345606235388472744304864750443815947483118515221858377162043183886293232627329219287661318319106934186887615984065115854765795923565075013577545904839607259373711394285994941080700892104508564388409^4+18311*1127578568759123461905472583562514487193426700832671937965946954795873451549610283245938900410992162601324566660559705062861591777483655250089731705035492319767414745810950331952452553599310408812053430351953439352301035104449117825335585761223641685411397632062^4=13251050629473965024889034724820586111661975958376246992911517463021247884586884222494690877338396697266589621353090560212164908808674193171340139790030962650992539846424211150135864818364129760979126378027620979749268808471509142010310345189210660539522388806599^4+18311*394992664242814900190474250614590172416594465560999970198807477132046914938925600796244683343359115128335679146380780059387680427489891537468250628824428642873830956308293038285491660533652666168846872859174355072068198028394826113401170707334084633480563349758^4

41365346191240427501836239189517178455535146582659406021245256392116666090687482611069696607551625046934598988812976805969187195201375032065986024854816998846455411442660784509364484920329798267376214383579372823861158998806248476704099650001723203678182621290924834480084605283600255^4+18311*22301069585312218969021049764046150429399846835280164893064904111558323718194420885520599605135274367934602783460316306600664133622756551787823080590017410016612376606875040369090367849207785979345924822008433245031020228676163794313609682038988593614585842372738361903646571796634592^4=223776457446704280526967136470896928461863081411280704011371476788613269945947836487583533420201042184838085482824142881642623159994646451939925405145189676563569905805502505288587115999011800495032593441689621065732862192687894149404373794093574193123911443266549050921554813812276929^4+18311*18234732915901970592119149631816016238673027571080123549185367087663143805196768864815808575453484996043949770764387265771210525220192652628607892807843185031635288807089786470736883501610436737911048302016066364273802703297535244064229016648089404040020562510733686194457918987515780^4

....

x=log[2026]8=log8/log(2026)=3*log(2)/(log(2)+log(1013))
y=log[1013]4=log(4)/log(1013)=2*log(2)/log(1013)
よって
3/x-2/y=(log(2)+log(1013))/log(2)-log(1013)/log(2)=log(2)/log(2)=1

x^4+20078*y^4=z^4+20078*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか求めた。

203583754762327689^4+20078*13433929914150867^4=208383223414477079^4+20078*12474036183720989^4

21821311652248057230420409435281528031277311652324201107166701487172711^4+20078*4747672214141794569619079487747874265172079173985805296651431020438379^4=25538972536743028540890672415143946398229906796537555142330431156276519^4+20078*4724384623656422584643136882337220620729364515786545953247995508251467^4

4466220437564308059643216762975137537992179616422418500703794815340617021784044146907138591689561129438012197447896433997608307316502211587571387116450564543^4+20078*322395838827387409792965189594563624982127442518416368483597822655491599388045273427764956274306050712959011279467066925548641422188039809890492308344697653^4=4789392796708457286144669858087474405606470814540860949183116225103398275707037071152405577874971782336863292574060273439240171486805671661798576745285362273^4+20078*257761366998557564492674570572096251459269202894727878787733540702935348603446688578711559037223920133188792254234299037222268588127347795045054382577738107^4

2120585420609611188145750707281799306298681010607996028785641178804190734451287092403248651870040321462140954652435071267768042588187717487060092179576416573629567996790836397676326762244108267522661385284270767020510421839414708708424920662665360888119904626385302402687819580533^4+20078*505622435947262068795150823782817281681600762265520231771799164027202964289027501911946110520346034631376962148241063729465086669956946261502840585919653943353807661646142195898607295221298151044670914338689970326556869683904910951226259390100105893682168755171404116088539496273^4=2910446274845081255662070566806342275105721406923439732268577486772155686390224332796549123588781464504232150294496893814099548306323475092241325376172765794333395764669796271214403723651334185764088960114212879219696131329868153671972020574846815657778800628154249948579027106037^4+20078*500583903143676419966413431034811034599279721240766920439044569088066319879274783128013444571418322561897658841145329286908431508945292254357442925230182530238785090645984337879538801957790339612679154741006758921484440949951661524853128857402329415497572295736506354164829841041^4

2200220050048624417731225827070120244808731423981636666230221935847436015167458567434231372070523140011762980386345345660466183166814843232243324150566400469218137036824035392589100216767840333553819397878305391250954172912391108525085449161948441515364326645255110723797305231204545715274795866177560338477569775871616584412178930150590806350750807555817129850853058124619173632589476415977248089601111277823992724761807216017741455825^4+20078*172592825136569575158884065163891272026497777708299201723063328129979215078148789164628020130455581331164702885307768350240215322424131450019531035455691068320116360644191667803866557443414403426939628424834602032411371719159819039911918033588732622563866482405054911587217639864874211141449347575069013344507993373990484177782159396821026183458691390643459826735569870551147555774339541451549402701706420910893847012357218351453407371^4=2471565979322361181093585830472402908971701770538000740789476306210540003309487824603936605013012452317746257821159593987048187923924303394220316405956388458932651540600955420343909847709223240021868282551296571313791378501215461882859338898594828328896669443675962659246767899726893232729846210216271911094101026978241302991257689586854077507880951893838909443128357702995814876895270909211045440127474698327728343471969702452440878415^4+20078*118323639281822222486412064483434739193903708397026386811212454057358417449742937730686973541957718869968047398344918684923814371002239417624132584377693470377213459888807662252904631255137822133329851490236366019843930601394948368357140086259455259857397922720884524497325106160404707650439278767326698821201743152665540461966407509568371952032662523039103908280509954875819306913180642804789932596433736810146723270324721064513522853^4

....

x^4+20078*y^4=z^4+20078*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか求めた。

223742512918749346609786179752161653286102353690960690697^4+20078*231046710546790758111592438948397244294413610762334214839^4=2573548143736256985655031537873968142562445249429601322913^4+20078*160587561256127181729281787405237170584976871860772557197^4

694021416105096410811890797144515236792589130770184482590320931506201450063552519242356481^4+20078*205408351012472883845049603752374267235099389266926570802855420415475552730971674339581677^4=2431703446247112995104367855632627358674564175181342723538563171127124985784742186575641729^4+20078*84205320677863213537029905995644419745229784801599802688518286188011703222559936882632531^4

15391952108343405846760430099944636086866950889991818369143491818288499394555128420721273714148388641238860282504192^4+20078*5164443622649267820659997704890104886621742058009353280441207470476700095084245461714087977874886990002748256103327^4=44282822065614040525422552583893239197354381697348612566801939648461743662541673852105153690446572592241693288635572^4+20078*4781352073010306574703832742416207660748480039880718542216364440648340414431888250423649922890939882244010672419967^4

424746565519647280358975443284135406980583512648933200167582096696929677740149650947319615640393052575510529449742413248424972560927127923453588493344448149552452748783717323846552416092^4+20078*31330637917362510020188765118448439819798751202711546366810906247040855690675450846732357354547617631927434604524456288567497375960849438452701075833077702741632372213705893589191235171^4=450240564291499697733177583113571183184339015097820651230272352281889404024371976478117823688836268520995621160872134193860146031079466203834773042858573421030505407456116627972473873344^4+20078*27081638122053773791155075146875810452506167461230304523029196982880901309971729924932656013140414974346585986002836130994968464268793058389170317580723490828623595768306009568204325629^4

1859117773633056785894011419216591803475677955053148161746748281824268216016661511055828904417613354310799988785267736442219861755009341654168239293325342348247746959260387497276323994177264071147912634232583835089866250934542569683966^4+20078*254794516145221838298152421428815084333918526208269498441207041044767597166457873113271873925370531883244611987709084779074839581355073799801420718612250648442063843225610068771192861874649704201788669392767347739966383099382249626153^4=3134265787291724106458690959157232726691198414228221409928059659548308546886018854845676219727318945165766769683644486519680339575762310705743165990061400139944198921987634741893307484255298158894895437798324103602193816105180681530922^4+20078*42269847202110618204039164772041597131331783012423957077655144757427542021564982481630654707086266740750148504646293099498093277896245624538932935822907683159321849437735528001695613528310689577291535465143969654578455570942564318327^4

11936452400198377296182679310083170820553869855781966420750437946576081455616025384930463240392091895482698722158343899539620196085372277293804534707033861968385100575927625101115481276586698769065696628116168418176141451517604243142812651017176817772499^4+20078*6749330641844278733635866462968217624438519262408577202235308179331659688060053086302927668401544417324554671740810783169389019478854495319202327896031293503147519432832752029444905473039743999446571148618059677801180378467807040915770738821556104269157^4=64122014147601803852982415253346265049017460046060717676508653892454052132459200921579852861767847243890607052210660028268969219503529299904457827089372741917168002565554304487177567723819130200445505118987588494670092983402137091502660163472402205550749^4+20078*5927080449455751457891649297603355020490035721231870147307873793840029243285817964782125015291778772570996290654023204798709216452629100880508065736703140477777997757414236235270602693694560828805295809232566474339858694018816514858474730260040399618051^4

27057898604659352292838790460043750337541616398937985721390821922420059170103201908354149052910051278654466556577177006239236476698851934509215419905841568226884159489120490943961935789677873565651526020142316298095889372616714360132967603915627383245897016129412058354800856659117713696345884315771286132794533319581261258892519265843886277284596922117^4+20078*4582902935080211453541273615247803872075334301097090632373696009648857021821018064671332061003318110693203442172845907895982417861314079553685777459365598710540378358154686738457916174630219002058283493224595534507026200159989383050725049151469980196440146406922562479947051403952523324184596430924813469783477462038287318146600520699484752994156727199^4=55360541580809099141743130311187293987347466807167868105212760886274882657971535132530077155633771165241400003027256455881239590628175508394605962081639938942842535383216163420738845753043359452858317991099639567931538207376738870887552626977234422923871771138859111864161565581942532389704834973025645273297538472199776678472649127901358021790996102413^4+20078*134204227611413021276116359942786736225640766941223098263293817660280226157037472691322622783968537071285465568834000377684767793573182760545979569934129742119350957527925341004902152597361979142848501934958343798915272300014702075039121358797859749888979427985279771613066749851613124708562011950913053633690063398131918450087789643427204423576469517^4

1657150029400362959337121815401697448874072378954654272428450936655339745129599999151545946490910307927213942107884512157843486993971779775237171392294069274700987391690204741099599864958923864643811204977673358732028060064457089003686438125884034172088152142758841746909858651784927165810088406618836195064867474027521608212538493117727222340554504433449328973363942^4+20078*198385108472752672464879261764710421880312082663456719275112509583713702421350903376779676794453580261315294592110845697150988924770780710509486513917448763780167271238311177011659887354300100306255897479025034659496965463814017554388063628471045266314843355835562773694477026359870016663983639293446033041712754668184533519484089676944866254861371755078136379026447^4=2489097635416388117387847613861708792260642888506878422770414554715693322381512937724936376637043495885131396306151390323923590659641652784417383934462066206853771885834276172273872096929755370180313359003021196297876941642746950866542077283642193421813060887671142211072835931050514620793159890133046144654706241209003915871999303037521826372010357031096588170968986^4+20078*59727174136748479456424962021375197982550331071419360884785239906988106212698746947881271770098048934995718892399699336137638313825801875646117756889449275088036522214299271815947848692494849383505538474800395065188818534099040577245457102178018724694025231683512696333980813148938774166805058707744374776739626804604148909573954690312432249618729655470259846092273^4

....

x^4+20078*y^4=z^4+20078*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか求めた。

37077057426433358^4+20078*5318345422336273^4=45998418015578786^4+20078*5089908598333393^4

1075444589480867400649396695836694447034562799521910485644157723210786^4+20078*82564180877232387257580375969290775570470777685811488087199510790987^4=1195843651757793929618824812013822399016372675484606104285735989572734^4+20078*57901391779181896540085759570691835074974077604000066994641799964619^4

12930624317913139987675763186998499068712092429027636349311674991826881001704856455603159317643719091152504918541282473017406384234064647342594812397486^4+20078*789730567669212259302854881287138152599860771611573248912683676737313499780853635810473559671165885045879391540176188441053795222992147970055221073049^4=13750551368541356008490007848372517525026851734293324925701689805587722928740317208320753763816453491416261386145419455398030469640999905925600976876194^4+20078*166850991397039764980430556982550046434025084531730090209000272650335415093850575693386627530357581928503153997983624336340971085098987043451970818777^4

2903013600036380629262322484901959698516893553007191960323897732649123890214535189256145371295630823123791437039558462663356653718449896865689812523229806313436401202972736130538901688655663317984814985947445288364706697077796407539148269888327674165588680924702061802554^4+20078*129371436900637271555331086548112257719436892161150791787805530023471491849158177768981754711962341712930962144042813667470525556012039868984474766698875338593981361799937677608243822618976966099849015736797545554495347205283168869503996252951113038674626797866917639223^4=2954320033415497059793055336498886741318438852755039985445264946858740144144011349174269062506949143141707199218384928992738809697133525783257761601072384810577253173408611788915690910721057917711301536629238120133542651685965083738818323149691700969244861666802831827462^4+20078*69513931291668102602809426351697374450967375788661429146210446778919195598102657864504114965424301692029239602078602949858010247547806131821867509215867091929654062958082742835323063542683266418948039941372575157520066829086379969888934114693081767742415932082685943497^4

423935102409258991005192486504807862863130592888194925008706486296063772794988472151136380987722583296820536803493117316494831875069221735850755553463664841937990528690285551048551643591430185161265196343310201427788382475495362937110215287504582614776455917965999301717837339225608875265765310190710445261488360579678510212395092271465545419216833971090093962972607297632376199242840793861537221911034155661939193072306^4+20078*21584382686398042057576675748087996025738312706982074791023306927393585461053494431422095085053408352295848723590554068723455257588183726519739006426565048460118558260410883288925674462175712073160820859479633910013675140395777117477526139430493106670372059537861829260215809986066351641538650761106459159454436563017311898089337960678298786144919459522267732065132770978123286318546310602205574356422744238871691915543^4=437497198061983976770897706408470388230557979557997433147041998108957542948783143716608463940488347929309387063392748759323023049126023328379106036120534263529006659131741193566472986797327636528647391766229534847491309437401919471238564003324720022015039490981798200944434805190391408522978454844867703455576680673779928875515951369956001606253500851091376358422230419118936469984965890493389726158647608608144852442494^4+20078*5761937758218891997587252527148383097073028258879148629631876479017520281626377605037998306826682947725523420374317385423898887855248535236663443326884056603933072745379300351350774055295352144548259532740411587026927018171461160994452637640332798225357891019429780162518766360486729508123315331256324599684729786565656791115002345772766567935474766187438270707239129243802970452733697865044319400873715801631755983657^4

....

x^4+20078*y^4=z^4+20078*w^4の別の自明でない整数解(0<x<z, 0<w<y, gcd(x,y,z,w)=1)をいくつか求めた。

24433864911378401731078620948852956976523614057444538800777553913437532634350642708143^4+20078*1932948863950424020190365559380997442010003472947963151257648070033338372191597624191^4=28232996226587748300494243726106693699755240520082300840861812990586941580277169313727^4+20078*508274620746919056659507017910846170798143549458802386226050916102310017469150147097^4

11881441458873703278586240734651498013856866521484167471210726616111822976262831473160505330242348941513510068008646174829789870896581289365276788552163451960018605117285555474285565826988152900555832238331338776749392556386302309949761922673763664461952765583063408760654841852867374505604374692146341122271993239072304141554745497531638^4+20078*2799704564006368200145856800224812337121295422353348000702985815401601033327019317773034277984895469198297435518184341208271381067459531047484271784951541935673765907373112193721138638199706420791327848519763940078646580607301982350557886686739976877056503999231791683245231700862383509119368908675349884851920048707010771850070766660093^4=26034707692922059295848173421592860717902013586958774837225451058141232683637949666573348733956899608248297654941505472156955900599428224679353308460709140726666404850167347505343253424041189673252423182067892474442477059973781112682414279180430194911871020912314442453946028843381362937511185371385196283046287818388100436383177695261414^4+20078*2507770273761765306327367957378198676895634727199629761552535850359427606938650004756781998408061030827247909581637895289415880071108069695294423180753091351819158992457559817925494210695182368969893755381443696556260108238002568674186747003259972041662841749237345951738963420580362152845685096039220800438440418536412838710591307488573^4

21115201321155611529002055590987777915980193024782170711769491378120754721278445410487820098242629415332641502283868601838175567003933342834926676480046649272959799391559544584429638053032093881207525460466622075324888482440858977127504334606086243142741514004035729554396244883333030121090865464896107519495546973387784714118388664577802169617666088742796890296054681161451026407200767758508892841351469591973248405349386116417632716874040993643282317885245032630374432168121835057712236506382103345137442380396381315310151929065844387108065598222474574758470356683231553243670444603838494401632503482530650174752618820093672718593950055060902892060082783091981041471262562167370223496946131637422305528583880826638001622424136229991927331366305746832564323^4+20078*2552618643060152040547726651262239351601031242976075430466507140768571173909727594951277707888956824888049509556241345677806303382026905774815823410252099478577621550141914904592559612491675280753518332801168031283674138540989045561363246391401023885530991237024087880739064872861895930057226371357808200148146888063731554838072011003644772766173887625461515645349707827880189082352585144084708493359002579241564543865186352826361647064552968377175325913143015973132033500551397477110176584581536547743150559832418937242110307819551267476292856294157290936462183978355396650761834742905182140973189110203610922142809920662813099052267927395910674122480441482415321108530640879918293266915357523810614426994742671748569963777885341274970591048856888594199753^4=31508098418021274959763868734215459532440933104914766650535967992015189317938348223264023216164773090884276885696043294256419205324875626086845168360946850068034269690820504073413593206968402482255523551427345831063374819323966961971249051932279572072874226611598355980818499543126139451933395056424784559539555905549523339082363238250162335074861091075930946692524604605652558908931739113485813637136096691424071683009324976392749364964046554368098125037754203191629775623574138694552349958091380567456728275892584315937430893590320287045986124876659812971516937719253406518468214239388259116852428241726404822411359498912975544805278936990754417132402870610975171064814140034834569891864972823844199121878124771670516599246728123555584859117252212727232339^4+20078*1344717768264471745987953277448141254571746287073648046570921589441841799837735959839798461331847053443813759223324163979035060988326450444653611045085475819575304812080944903776423570234440444639480951309103377118258237790176448755041022605921474463268775990811897029169280624560520069008722225465445689868356461496920429523418454123490289280274238249463755503326513463695385605796529114031636805060232583052494185257290719664307095969199116894630601769047922987338720295243216386704865959809442410626581650978657187993119303877127195000427341201162173393430283910152798327287328870425979627234282674494797070729217833894425460776980403327783647779639591337207477489051200820380836631179207921097595670490598807638623152530586618811400981857748036116300753^4

....

-bash-3.1$ time ./dqde4 20006 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20006, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 82012419
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
89^4+20006*68^4=551^4+20006*64^4
709^4+20006*92^4=877^4+20006*86^4
6943^4+20006*512^4=7657^4+20006*338^4
5739^4+20006*684^4=8597^4+20006*92^4
7277^4+20006*956^4=11819^4+20006*98^4
12991^4+20006*1549^4=19153^4+20006*821^4
6449^4+20006*2278^4=27113^4+20006*244^4
10347^4+20006*5758^4=66093^4+20006*3476^4
63022^4+20006*7063^4=87662^4+20006*4247^4
198239^4+20006*10039^4=204457^4+20006*1579^4
228707^4+20006*13600^4=240005^4+20006*8458^4
84011^4+20006*17113^4=187429^4+20006*12767^4
150061^4+20006*21499^4=230053^4+20006*17737^4
178508^4+20006*24259^4=298544^4+20006*1763^4
35729^4+20006*26527^4=241879^4+20006*23861^4
343449^4+20006*31426^4=427503^4+20006*5992^4
86048^4+20006*35747^4=425316^4+20006*387^4
355655^4+20006*36797^4=453025^4+20006*26953^4
17337^4+20006*39339^4=417457^4+20006*30601^4
121257^4+20006*42648^4=304727^4+20006*41224^4
96726^4+20006*49053^4=583478^4+20006*5149^4
230663^4+20006*49606^4=564857^4+20006*32446^4
737988^4+20006*55561^4=830628^4+20006*27383^4
451547^4+20006*58957^4=700747^4+20006*38101^4
338902^4+20006*61481^4=739302^4+20006*11031^4
130093^4+20006*83822^4=992339^4+20006*30886^4

Found 26 solutions.
Search finished successfully.

real 49m15.487s
user 49m8.407s
sys 0m6.854s

-bash-3.1$ time ./dqde4 20007 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20007, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / C...
Total nodes collected after filter: 3550130
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
732^4+20007*199^4=2346^4+20007*91^4
3519^4+20007*371^4=4803^4+20007*57^4
2037^4+20007*419^4=5001^4+20007*143^4
4422^4+20007*457^4=5952^4+20007*19^4
1902^4+20007*649^4=7716^4+20007*173^4
1164^4+20007*789^4=8298^4+20007*623^4
37863^4+20007*1144^4=37977^4+20007*828^4
8433^4+20007*1202^4=14709^4+20007*156^4
6069^4+20007*1214^4=12171^4+20007*1034^4
41817^4+20007*1424^4=42087^4+20007*596^4
9189^4+20007*1771^4=12153^4+20007*1737^4
9141^4+20007*1802^4=15753^4+20007*1672^4
15891^4+20007*3554^4=25377^4+20007*3452^4
33138^4+20007*3659^4=46704^4+20007*1143^4
21678^4+20007*5307^4=63252^4+20007*1433^4
17901^4+20007*5723^4=66573^4+20007*3131^4
20211^4+20007*6509^4=77097^4+20007*2473^4
56783^4+20007*7546^4=92747^4+20007*2824^4
5349^4+20007*8149^4=42987^4+20007*8069^4

Found 19 solutions.
Search finished successfully.

real 0m14.609s
user 0m14.296s
sys 0m0.311s

-bash-3.1$ time ./dqde4 20008 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20008, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / C...
Total nodes collected after filter: 3251195
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
216^4+20008*67^4=796^4+20008*21^4
502^4+20008*83^4=746^4+20008*77^4
186^4+20008*109^4=1278^4+20008*53^4
1503^4+20008*217^4=1889^4+20008*207^4
138^4+20008*601^4=4826^4+20008*567^4
8134^4+20008*601^4=8954^4+20008*409^4
4053^4+20008*976^4=9909^4+20008*814^4
2573^4+20008*1047^4=12333^4+20008*467^4
18594^4+20008*1903^4=24826^4+20008*567^4
1063^4+20008*2344^4=25639^4+20008*1712^4
13666^4+20008*2607^4=30722^4+20008*1359^4
25527^4+20008*2816^4=33353^4+20008*2172^4
20177^4+20008*2909^4=35183^4+20008*1349^4
39209^4+20008*3371^4=46999^4+20008*1357^4
25204^4+20008*3513^4=34088^4+20008*3201^4
28887^4+20008*3589^4=41289^4+20008*2729^4
51426^4+20008*4399^4=61638^4+20008*1271^4
73514^4+20008*4759^4=79262^4+20008*31^4
31651^4+20008*5268^4=41411^4+20008*5094^4
20173^4+20008*5518^4=65773^4+20008*68^4
27386^4+20008*6671^4=79394^4+20008*2183^4
72452^4+20008*7149^4=73672^4+20008*7083^4
18182^4+20008*9109^4=94594^4+20008*7331^4
50259^4+20008*29287^4=71731^4+20008*29277^4

Found 24 solutions.
Search finished successfully.

real 0m16.006s
user 0m15.692s
sys 0m0.312s

-bash-3.1$ time ./dqde4 20009 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20009, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 138993605
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
887^4+20009*119^4=1467^4+20009*3^4
1541^4+20009*667^4=6249^4+20009*591^4
33351^4+20009*853^4=33417^4+20009*443^4
4099^4+20009*1006^4=11161^4+20009*716^4
33010^4+20009*2305^4=36112^4+20009*1267^4
40889^4+20009*4543^4=56725^4+20009*2635^4
7673^4+20009*6932^4=81351^4+20009*3312^4
57647^4+20009*8054^4=98787^4+20009*288^4
202322^4+20009*18377^4=237876^4+20009*13941^4
108017^4+20009*25006^4=298691^4+20009*1516^4
20360^4+20009*26317^4=311400^4+20009*9933^4
172339^4+20009*26749^4=207649^4+20009*26087^4
425767^4+20009*34441^4=461933^4+20009*29659^4
282323^4+20009*36097^4=360319^4+20009*32909^4
321437^4+20009*48094^4=376007^4+20009*47012^4
429383^4+20009*48278^4=608731^4+20009*22772^4
687337^4+20009*48873^4=734479^4+20009*39009^4
564505^4+20009*53774^4=718425^4+20009*18726^4
111011^4+20009*55663^4=577103^4+20009*44899^4
518953^4+20009*61199^4=768257^4+20009*22183^4
50861^4+20009*72563^4=862991^4+20009*8071^4
338271^4+20009*81699^4=771319^4+20009*72427^4

Found 22 solutions.
Search finished successfully.

real 47m48.191s
user 47m34.089s
sys 0m14.100s

-bash-3.1$ time ./dqde4 20010 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20010, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 336045175
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
379^4+20010*40^4=517^4+20010*12^4
4450^4+20010*781^4=8890^4+20010*531^4
14951^4+20010*1243^4=16193^4+20010*1097^4
5903^4+20010*1311^4=15671^4+20010*163^4
20031^4+20010*1636^4=23481^4+20010*362^4
3623^4+20010*1854^4=21977^4+20010*638^4
5003^4+20010*2753^4=11971^4+20010*2741^4
1843^4+20010*3477^4=9059^4+20010*3475^4
3375^4+20010*3487^4=40785^4+20010*1759^4
2078^4+20010*4253^4=45946^4+20010*3197^4
2762^4+20010*4441^4=51062^4+20010*2649^4
78881^4+20010*6180^4=87713^4+20010*4568^4
53540^4+20010*6369^4=77560^4+20010*3967^4
37090^4+20010*9097^4=107810^4+20010*3721^4
32873^4+20010*9400^4=111521^4+20010*3414^4
159719^4+20010*11331^4=176831^4+20010*3457^4
134897^4+20010*12183^4=166679^4+20010*1589^4
82873^4+20010*13565^4=163511^4+20010*4715^4
98785^4+20010*14148^4=161575^4+20010*10186^4
21649^4+20010*14684^4=135407^4+20010*13128^4
656953^4+20010*22416^4=661361^4+20010*3310^4
198782^4+20010*23197^4=284126^4+20010*14307^4
162503^4+20010*23664^4=288911^4+20010*3970^4
161669^4+20010*27055^4=302659^4+20010*19699^4
62333^4+20010*28840^4=205163^4+20010*27878^4
191449^4+20010*28907^4=346193^4+20010*14767^4
195337^4+20010*32058^4=331409^4+20010*26932^4
378502^4+20010*33353^4=453914^4+20010*19401^4
117061^4+20010*35691^4=385949^4+20010*26895^4
405031^4+20010*37949^4=506183^4+20010*19277^4
117408^4+20010*39139^4=299844^4+20010*37379^4
43387^4+20010*40062^4=390163^4+20010*34508^4
65389^4+20010*41264^4=487301^4+20010*16930^4
498183^4+20010*47069^4=506319^4+20010*46567^4
479935^4+20010*48039^4=623225^4+20010*25723^4
502511^4+20010*49353^4=653023^4+20010*13313^4
483884^4+20010*55779^4=700984^4+20010*24381^4
147957^4+20010*57710^4=265077^4+20010*57418^4
68267^4+20010*63161^4=716821^4+20010*40615^4
225595^4+20010*63916^4=760645^4+20010*17288^4
792746^4+20010*66091^4=938786^4+20010*3765^4
665356^4+20010*71565^4=920816^4+20010*17581^4
419821^4+20010*73165^4=878717^4+20010*25349^4
435333^4+20010*75367^4=837717^4+20010*55441^4
521947^4+20010*80163^4=676829^4+20010*76649^4
37215^4+20010*81242^4=576105^4+20010*78544^4
88677^4+20010*83152^4=988989^4+20010*1882^4
24775^4+20010*95638^4=515135^4+20010*94616^4

Found 48 solutions.
Search finished successfully.

real 165m40.157s
user 59m13.941s
sys 1m47.371s

(続く)

-bash-3.1$ time ./dqde4 20011 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20011, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 13424030
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
119468^4+20011*4819^4=120664^4+20011*3347^4
48159^4+20011*9898^4=88181^4+20011*9096^4

Found 2 solutions.
Search finished successfully.

real 32m56.860s
user 32m55.777s
sys 0m1.081s

-bash-3.1$ time ./dqde4 20012 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20012, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 22173841
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
685243^4+20012*110194^4=765627^4+20012*109026^4

Found 1 solutions.
Search finished successfully.

real 41m11.528s
user 41m9.917s
sys 0m1.611s

-bash-3.1$ time ./dqde4 20013 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20013, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 104587169
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
10697^4+20013*724^4=11677^4+20013*46^4
9253^4+20013*1568^4=17431^4+20013*1158^4
7618^4+20013*4101^4=43832^4+20013*3151^4
48731^4+20013*11812^4=131863^4+20013*8254^4
223939^4+20013*13452^4=237281^4+20013*1922^4
16929^4+20013*18289^4=217059^4+20013*5579^4
4166^4+20013*25043^4=148492^4+20013*24647^4
93121^4+20013*27689^4=327467^4+20013*11413^4
39951^4+20013*39281^4=463083^4+20013*16979^4
345753^4+20013*72755^4=513921^4+20013*70885^4

Found 10 solutions.
Search finished successfully.

real 56m57.804s
user 56m47.466s
sys 0m10.337s

-bash-3.1$ time ./dqde4 20014 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20014, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / C...
Total nodes collected after filter: 21721034
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
19932^4+20014*769^4=20096^4+20014*543^4
55757^4+20014*22342^4=155827^4+20014*21662^4
298123^4+20014*42922^4=522451^4+20014*16036^4
56829^4+20014*127877^4=957459^4+20014*122531^4

Found 4 solutions.
Search finished successfully.

real 51m15.748s
user 51m13.526s
sys 0m2.132s

-bash-3.1$ time ./dqde4 20015 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20015, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 81960716
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
134542^4+20015*6671^4=137662^4+20015*4495^4
274633^4+20015*18215^4=297796^4+20015*6082^4
74257^4+20015*20319^4=174332^4+20015*18834^4
115664^4+20015*33632^4=400723^4+20015*2543^4
980969^4+20015*42556^4=996981^4+20015*20718^4
305077^4+20015*52089^4=579586^4+20015*38322^4
707535^4+20015*61401^4=787595^4+20015*52349^4
353848^4+20015*62366^4=742139^4+20015*29483^4
738463^4+20015*70955^4=946619^4+20015*17161^4
406363^4+20015*77878^4=934759^4+20015*5524^4

Found 10 solutions.
Search finished successfully.

real 48m25.337s
user 48m16.853s
sys 0m8.295s

(続く)

-bash-3.1$ time ./dqde4 20016 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20016, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 248193985
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
714^4+20016*73^4=954^4+20016*1^4
3004^4+20016*163^4=3112^4+20016*97^4
1809^4+20016*226^4=2643^4+20016*163^4
5563^4+20016*531^4=6391^4+20016*458^4
4740^4+20016*551^4=6936^4+20016*205^4
5231^4+20016*578^4=7279^4+20016*306^4
16079^4+20016*749^4=16357^4+20016*528^4
537^4+20016*904^4=8043^4+20016*823^4
3028^4+20016*931^4=10256^4+20016*671^4
1588^4+20016*1129^4=13424^4+20016*227^4
336^4+20016*1795^4=21348^4+20016*265^4
6735^4+20016*2102^4=21747^4+20016*1705^4
4053^4+20016*2290^4=22635^4+20016*1948^4
26004^4+20016*2519^4=32376^4+20016*1693^4
200139^4+20016*2998^4=200181^4+20016*1916^4
28748^4+20016*3255^4=33752^4+20016*3005^4
19804^4+20016*5539^4=43024^4+20016*5281^4
120462^4+20016*7495^4=128070^4+20016*3917^4
29756^4+20016*8617^4=74216^4+20016*7971^4
61011^4+20016*10418^4=123303^4+20016*5513^4
77352^4+20016*11891^4=144492^4+20016*1447^4
77032^4+20016*12621^4=92548^4+20016*12377^4
286863^4+20016*22534^4=327729^4+20016*11864^4
465995^4+20016*24688^4=472255^4+20016*22187^4
42543^4+20016*24797^4=291909^4+20016*11158^4
28323^4+20016*25897^4=200193^4+20016*24656^4
199266^4+20016*30581^4=297798^4+20016*27361^4
256856^4+20016*31447^4=390884^4+20016*13061^4
65076^4+20016*32755^4=388668^4+20016*10445^4
139903^4+20016*33978^4=405533^4+20016*5311^4
439529^4+20016*34286^4=504859^4+20016*5241^4
13235^4+20016*37453^4=241969^4+20016*36610^4
489796^4+20016*38161^4=562156^4+20016*9007^4
317190^4+20016*38377^4=446754^4+20016*28765^4
620935^4+20016*39827^4=665971^4+20016*18430^4
419910^4+20016*40663^4=464130^4+20016*37459^4
919536^4+20016*49087^4=923604^4+20016*47683^4
373053^4+20016*55478^4=676119^4+20016*3611^4
135706^4+20016*55551^4=602662^4+20016*41441^4
455645^4+20016*55708^4=695837^4+20016*16370^4
48937^4+20016*58353^4=644413^4+20016*41546^4
243589^4+20016*62404^4=728977^4+20016*33321^4
103806^4+20016*63629^4=440742^4+20016*61721^4
83852^4+20016*66741^4=793864^4+20016*5337^4
72726^4+20016*68231^4=811314^4+20016*13021^4
711014^4+20016*73503^4=911174^4+20016*52367^4
557795^4+20016*82531^4=958115^4+20016*54969^4
454427^4+20016*85107^4=461861^4+20016*85049^4
390367^4+20016*86182^4=402877^4+20016*86121^4

Found 49 solutions.
Search finished successfully.

real 108m53.301s
user 61m46.912s
sys 1m2.017s

-bash-3.1$ time ./dqde4 20017 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20017, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 1444212
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
269^4+20017*176^4=2086^4+20017*61^4
1874^4+20017*259^4=3178^4+20017*67^4
2221^4+20017*476^4=5692^4+20017*103^4
4152^4+20017*721^4=6668^4+20017*657^4
8039^4+20017*822^4=9573^4+20017*704^4
4187^4+20017*970^4=11062^4+20017*625^4
1384^4+20017*1217^4=4567^4+20017*1214^4
3629^4+20017*1360^4=16129^4+20017*470^4
1078^4+20017*1579^4=18727^4+20017*518^4
9301^4+20017*1734^4=10383^4+20017*1724^4
3637^4+20017*1816^4=5801^4+20017*1814^4
7740^4+20017*1897^4=22205^4+20017*996^4
7463^4+20017*2277^4=21819^4+20017*1991^4
48136^4+20017*3093^4=51801^4+20017*392^4
84982^4+20017*4469^4=87056^4+20017*3409^4
45039^4+20017*6121^4=74619^4+20017*2789^4
34916^4+20017*6207^4=74409^4+20017*2282^4
53408^4+20017*7291^4=89002^4+20017*3143^4
32309^4+20017*8542^4=74936^4+20017*7853^4

Found 19 solutions.
Search finished successfully.

real 0m16.323s
user 0m16.097s
sys 0m0.221s

-bash-3.1$ time ./dqde4 20018 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20018, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 18482079
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
133577^4+20018*11323^4=152033^4+20018*8671^4
129271^4+20018*16993^4=198353^4+20018*11893^4
737691^4+20018*18471^4=738253^4+20018*16339^4

Found 3 solutions.
Search finished successfully.

real 37m10.538s
user 37m9.187s
sys 0m1.351s

-bash-3.1$ time ./dqde4 20019 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20019, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 64312649
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
389^4+20019*27^4=427^4+20019*11^4
197^4+20019*48^4=367^4+20019*46^4
247^4+20019*117^4=1369^4+20019*59^4
889^4+20019*549^4=4441^4+20019*517^4
4009^4+20019*779^4=9337^4+20019*197^4
10578^4+20019*2981^4=34152^4+20019*1847^4
84021^4+20019*3227^4=84921^4+20019*473^4
48904^4+20019*3431^4=52652^4+20019*2521^4
18006^4+20019*3589^4=39012^4+20019*2729^4
42467^4+20019*5339^4=64301^4+20019*3317^4
22402^4+20019*8447^4=97712^4+20019*4843^4
8306^4+20019*24619^4=258614^4+20019*19477^4
34399^4+20019*27308^4=274627^4+20019*22838^4
454342^4+20019*36353^4=519916^4+20019*21781^4
121829^4+20019*42837^4=504991^4+20019*18977^4
646097^4+20019*46153^4=716683^4+20019*15869^4
691095^4+20019*53425^4=790311^4+20019*15263^4
416714^4+20019*102279^4=688832^4+20019*99923^4

Found 18 solutions.
Search finished successfully.

real 49m33.212s
user 49m28.309s
sys 0m4.903s

-bash-3.1$ time ./dqde4 20020 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20020, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 4089125
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2474^4+20020*353^4=3818^4+20020*287^4
1994^4+20020*455^4=5426^4+20020*137^4
30332^4+20020*509^4=30344^4+20020*115^4
11764^4+20020*573^4=11952^4+20020*461^4
8049^4+20020*683^4=9617^4+20020*45^4
5967^4+20020*701^4=7969^4+20020*567^4
2451^4+20020*1214^4=13693^4+20020*804^4
7039^4+20020*1855^4=13969^4+20020*1781^4
58057^4+20020*2070^4=58521^4+20020*76^4
22822^4+20020*3285^4=36066^4+20020*2597^4
44533^4+20020*3348^4=50331^4+20020*1118^4
1487^4+20020*4353^4=51537^4+20020*1607^4
22816^4+20020*5675^4=36236^4+20020*5573^4
26714^4+20020*6327^4=62386^4+20020*5433^4
47681^4+20020*6975^4=82449^4+20020*4219^4
48236^4+20020*7751^4=93136^4+20020*3319^4
15418^4+20020*9003^4=91494^4+20020*7445^4
33741^4+20020*10334^4=86563^4+20020*9648^4

Found 18 solutions.
Search finished successfully.

real 0m23.373s
user 0m22.875s
sys 0m0.481s

(続く)

-bash-3.1$ time ./dqde4 20021 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20021, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 43917017
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
48591^4+20021*617^4=48597^4+20021*293^4
1427^4+20021*1042^4=9709^4+20021*926^4
711122^4+20021*19463^4=712898^4+20021*11143^4
484467^4+20021*36396^4=505873^4+20021*33338^4
92881^4+20021*41087^4=488897^4+20021*943^4
47869^4+20021*55661^4=589383^4+20021*43473^4
99821^4+20021*121831^4=140431^4+20021*121829^4

Found 7 solutions.
Search finished successfully.

real 50m42.115s
user 50m38.727s
sys 0m3.282s

-bash-3.1$ time ./dqde4 20022 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20022, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 55108354
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
15661^4+20022*2458^4=20549^4+20022*2352^4
118502^4+20022*7251^4=126022^4+20022*2003^4
2379^4+20022*18715^4=222621^4+20022*895^4
64034^4+20022*24187^4=269666^4+20022*16763^4
135067^4+20022*24272^4=292069^4+20022*3996^4
124259^4+20022*25780^4=307013^4+20022*9970^4
318926^4+20022*61507^4=455258^4+20022*59677^4
352299^4+20022*63991^4=769779^4+20022*3133^4

Found 8 solutions.
Search finished successfully.

real 53m9.616s
user 53m4.998s
sys 0m4.483s

-bash-3.1$ time ./dqde4 20023 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20023, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 14610792
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
101669^4+20023*10937^4=138607^4+20023*5899^4
30659^4+20023*18237^4=110751^4+20023*17921^4
161684^4+20023*23813^4=278822^4+20023*15233^4
252373^4+20023*95214^4=772971^4+20023*89638^4

Found 4 solutions.
Search finished successfully.

real 29m49.559s
user 29m47.955s
sys 0m1.171s

-bash-3.1$ time ./dqde4 20024 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20024, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 34291675
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
10008^4+20024*201^4=10016^4+20024*73^4
30686^4+20024*5351^4=60722^4+20024*3689^4
147387^4+20024*12189^4=172997^4+20024*5491^4
2857^4+20024*13906^4=152329^4+20024*10124^4
55504^4+20024*16541^4=104688^4+20024*16227^4
722454^4+20024*30771^4=729286^4+20024*24739^4
643480^4+20024*55225^4=763624^4+20024*30649^4
678108^4+20024*57729^4=803668^4+20024*30209^4
404863^4+20024*84479^4=760289^4+20024*77237^4
466542^4+20024*95217^4=905102^4+20024*84527^4

Found 10 solutions.
Search finished successfully.

real 47m26.989s
user 47m23.855s
sys 0m2.922s

-bash-3.1$ time ./dqde4 20025 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20025, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 3323853
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
35^4+20025*13^4=145^4+20025*9^4
109^4+20025*24^4=287^4+20025*2^4
117^4+20025*35^4=417^4+20025*1^4
145^4+20025*148^4=1745^4+20025*64^4
3860^4+20025*191^4=3970^4+20025*59^4
2587^4+20025*222^4=3109^4+20025*10^4
129^4+20025*235^4=1197^4+20025*233^4
6913^4+20025*407^4=7291^4+20025*139^4
4300^4+20025*603^4=7360^4+20025*229^4
21545^4+20025*837^4=21745^4+20025*541^4
7199^4+20025*842^4=8801^4+20025*762^4
7669^4+20025*1124^4=12169^4+20025*906^4
12285^4+20025*1439^4=16185^4+20025*1189^4
21225^4+20025*1498^4=23445^4+20025*536^4
5979^4+20025*1975^4=22329^4+20025*1301^4
13329^4+20025*2293^4=26079^4+20025*1573^4
40401^4+20025*2330^4=41199^4+20025*2078^4
20844^4+20025*2615^4=22944^4+20025*2551^4
34485^4+20025*2638^4=36405^4+20025*2366^4
57771^4+20025*5557^4=74121^4+20025*1265^4
48183^4+20025*6005^4=69831^4+20025*4421^4
12470^4+20025*10537^4=60530^4+20025*10391^4

Found 22 solutions.
Search finished successfully.

real 0m18.336s
user 0m17.993s
sys 0m0.341s

(続く)

-bash-3.1$ time ./dqde4 20026 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20026, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 140041598
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
148^4+20026*19^4=224^4+20026*13^4
4817^4+20026*185^4=4855^4+20026*133^4
23291^4+20026*2779^4=33253^4+20026*1909^4
55313^4+20026*4572^4=58953^4+20026*4166^4
12261^4+20026*6197^4=73733^4+20026*357^4
66322^4+20026*6451^4=85702^4+20026*1427^4
59511^4+20026*7382^4=69201^4+20026*7036^4
190957^4+20026*9081^4=195669^4+20026*707^4
218654^4+20026*9137^4=221918^4+20026*689^4
31063^4+20026*10076^4=118049^4+20026*5062^4
76403^4+20026*11713^4=119989^4+20026*10043^4
33259^4+20026*11768^4=73939^4+20026*11542^4
82694^4+20026*11939^4=99338^4+20026*11549^4
96766^4+20026*13889^4=136478^4+20026*12481^4
21961^4+20026*18404^4=61367^4+20026*18376^4
172207^4+20026*19446^4=223791^4+20026*15758^4
531133^4+20026*23351^4=540619^4+20026*8699^4
54391^4+20026*27042^4=308433^4+20026*16988^4
390625^4+20026*40876^4=444007^4+20026*37670^4
133717^4+20026*47533^4=565891^4+20026*703^4
5949^4+20026*57584^4=442987^4+20026*54882^4
422319^4+20026*62557^4=762761^4+20026*3303^4
726923^4+20026*68357^4=841189^4+20026*57293^4
113189^4+20026*74478^4=330917^4+20026*74118^4
330279^4+20026*78482^4=937249^4+20026*4272^4

Found 25 solutions.
Search finished successfully.

real 54m30.598s
user 54m17.148s
sys 0m13.439s

-bash-3.1$ time ./dqde4 20026 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20026, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 140041598
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
148^4+20026*19^4=224^4+20026*13^4
4817^4+20026*185^4=4855^4+20026*133^4
23291^4+20026*2779^4=33253^4+20026*1909^4
55313^4+20026*4572^4=58953^4+20026*4166^4
12261^4+20026*6197^4=73733^4+20026*357^4
66322^4+20026*6451^4=85702^4+20026*1427^4
59511^4+20026*7382^4=69201^4+20026*7036^4
190957^4+20026*9081^4=195669^4+20026*707^4
218654^4+20026*9137^4=221918^4+20026*689^4
31063^4+20026*10076^4=118049^4+20026*5062^4
76403^4+20026*11713^4=119989^4+20026*10043^4
33259^4+20026*11768^4=73939^4+20026*11542^4
82694^4+20026*11939^4=99338^4+20026*11549^4
96766^4+20026*13889^4=136478^4+20026*12481^4
21961^4+20026*18404^4=61367^4+20026*18376^4
172207^4+20026*19446^4=223791^4+20026*15758^4
531133^4+20026*23351^4=540619^4+20026*8699^4
54391^4+20026*27042^4=308433^4+20026*16988^4
390625^4+20026*40876^4=444007^4+20026*37670^4
133717^4+20026*47533^4=565891^4+20026*703^4
5949^4+20026*57584^4=442987^4+20026*54882^4
422319^4+20026*62557^4=762761^4+20026*3303^4
726923^4+20026*68357^4=841189^4+20026*57293^4
113189^4+20026*74478^4=330917^4+20026*74118^4
330279^4+20026*78482^4=937249^4+20026*4272^4

Found 25 solutions.
Search finished successfully.

real 43m33.276s
user 43m21.830s
sys 0m11.187s

-bash-3.1$ time ./dqde4 20027 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20027, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 62541772
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2223^4+20027*199^4=2733^4+20027*37^4
7283^4+20027*524^4=8089^4+20027*214^4
6873^4+20027*2061^4=24527^4+20027*539^4
58393^4+20027*5716^4=75559^4+20027*2128^4
59899^4+20027*6374^4=81641^4+20027*2944^4
164637^4+20027*23663^4=284799^4+20027*12139^4
346213^4+20027*25666^4=386267^4+20027*14122^4
126114^4+20027*34371^4=406492^4+20027*14561^4
635672^4+20027*54061^4=696166^4+20027*47207^4
277835^4+20027*75139^4=609075^4+20027*70923^4

Found 10 solutions.
Search finished successfully.

real 45m14.587s
user 45m10.636s
sys 0m3.933s

-bash-3.1$ time ./dqde4 20028 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20028, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 46804571
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
14789^4+20028*2554^4=27403^4+20028*2024^4
40681^4+20028*6998^4=77801^4+20028*5154^4
146071^4+20028*9651^4=157687^4+20028*4811^4
41237^4+20028*13502^4=55621^4+20028*13468^4
87927^4+20028*17194^4=162423^4+20028*15358^4
399534^4+20028*27041^4=436014^4+20028*7007^4
100510^4+20028*27829^4=331750^4+20028*3003^4
275582^4+20028*31231^4=393938^4+20028*13857^4
22907^4+20028*66114^4=763573^4+20028*38216^4
736592^4+20028*69999^4=938332^4+20028*3361^4
379922^4+20028*96907^4=941926^4+20028*84059^4
41826^4+20028*125539^4=341622^4+20028*125453^4

Found 12 solutions.
Search finished successfully.

real 44m46.265s
user 44m42.559s
sys 0m3.703s

-bash-3.1$ time ./dqde4 20029 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20029, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 43899452
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
53^4+20029*17^4=193^4+20029*11^4
5704^4+20029*1691^4=9434^4+20029*1673^4
408161^4+20029*13569^4=409291^4+20029*11661^4
362902^4+20029*37131^4=484878^4+20029*9163^4
569411^4+20029*49922^4=609469^4+20029*46238^4
28085^4+20029*58150^4=690293^4+20029*17678^4

Found 6 solutions.
Search finished successfully.

real 44m56.069s
user 44m52.567s
sys 0m3.503s

-bash-3.1$ time ./dqde4 20030 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20030, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 52408025
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1801^4+20030*487^4=5807^4+20030*43^4
2647^4+20030*1736^4=18671^4+20030*1318^4
92641^4+20030*11540^4=143713^4+20030*3280^4
98423^4+20030*14533^4=161967^4+20030*11055^4
86559^4+20030*28978^4=338937^4+20030*14884^4
277376^4+20030*55673^4=571896^4+20030*46215^4
72208^4+20030*63367^4=712968^4+20030*42375^4

Found 7 solutions.
Search finished successfully.

real 51m11.738s
user 51m6.964s
sys 0m4.773s

(続く)

-bash-3.1$ time ./dqde4 20031 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20031, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 140641391
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
817^4+20031*83^4=1004^4+20031*66^4
30604^4+20031*878^4=30703^4+20031*397^4
16479^4+20031*2494^4=23583^4+20031*2278^4
73996^4+20031*3200^4=74603^4+20031*2725^4
1511^4+20031*3501^4=31874^4+20031*3152^4
170178^4+20031*3718^4=170349^4+20031*2179^4
1791^4+20031*3979^4=43734^4+20031*2872^4
73859^4+20031*4979^4=80536^4+20031*332^4
6836^4+20031*5316^4=62969^4+20031*1929^4
166502^4+20031*17074^4=222953^4+20031*441^4
483937^4+20031*24629^4=499403^4+20031*5287^4
269200^4+20031*26419^4=349940^4+20031*5133^4
79483^4+20031*26569^4=281614^4+20031*20776^4
520708^4+20031*27832^4=540739^4+20031*6579^4
167785^4+20031*42607^4=459853^4+20031*32405^4
572323^4+20031*43497^4=649568^4+20031*14806^4
853126^4+20031*53636^4=913219^4+20031*3169^4
256957^4+20031*85751^4=757732^4+20031*78426^4
64607^4+20031*105054^4=663109^4+20031*102908^4

Found 19 solutions.
Search finished successfully.

real 45m12.987s
user 44m59.338s
sys 0m13.649s

-bash-3.1$ time ./dqde4 20032 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20032, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 197261133
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2063^4+20032*243^4=2319^4+20032*233^4
1046^4+20032*297^4=2646^4+20032*271^4
22824^4+20032*521^4=22848^4+20032*359^4
5948^4+20032*725^4=9052^4+20032*245^4
7747^4+20032*733^4=9149^4+20032*587^4
25001^4+20032*1337^4=25943^4+20032*541^4
5102^4+20032*2201^4=24946^4+20032*1429^4
841^4+20032*4086^4=48569^4+20032*987^4
22406^4+20032*4271^4=49574^4+20032*2573^4
200021^4+20032*4527^4=200283^4+20032*844^4
54257^4+20032*5745^4=68351^4+20032*4560^4
51188^4+20032*6181^4=77468^4+20032*1451^4
11024^4+20032*6357^4=60256^4+20032*5589^4
120532^4+20032*6543^4=123684^4+20032*5119^4
37621^4+20032*6555^4=78603^4+20032*2525^4
81268^4+20032*7757^4=103804^4+20032*1187^4
63737^4+20032*10592^4=101783^4+20032*9473^4
41011^4+20032*10716^4=86067^4+20032*10144^4
4094^4+20032*10945^4=128642^4+20032*5105^4
70479^4+20032*11161^4=133553^4+20032*5427^4
51652^4+20032*11439^4=136788^4+20032*671^4
69912^4+20032*12607^4=145032^4+20032*8129^4
62387^4+20032*12616^4=92339^4+20032*12242^4
45952^4+20032*12881^4=132176^4+20032*10577^4
500446^4+20032*13721^4=501698^4+20032*7949^4
7718^4+20032*14709^4=147942^4+20032*12301^4
161741^4+20032*15744^4=208893^4+20032*4843^4
42244^4+20032*17623^4=189716^4+20032*13369^4
117851^4+20032*19827^4=239451^4+20032*2689^4
102833^4+20032*20492^4=228959^4+20032*14543^4
196646^4+20032*20991^4=270886^4+20032*321^4
249426^4+20032*21649^4=301042^4+20032*7323^4
151926^4+20032*22333^4=272502^4+20032*3101^4
165198^4+20032*25703^4=232018^4+20032*23949^4
127186^4+20032*31767^4=373614^4+20032*15569^4
209921^4+20032*32224^4=332047^4+20032*27457^4
83554^4+20032*32411^4=374018^4+20032*18953^4
261824^4+20032*33653^4=414256^4+20032*14731^4
128718^4+20032*35183^4=342738^4+20032*30427^4
293052^4+20032*36721^4=433596^4+20032*25487^4
125664^4+20032*36979^4=395168^4+20032*28557^4
765448^4+20032*37617^4=786888^4+20032*3313^4
189824^4+20032*37841^4=453704^4+20032*319^4
469340^4+20032*38773^4=523580^4+20032*31061^4
500776^4+20032*40279^4=582832^4+20032*10297^4
703269^4+20032*44492^4=753189^4+20032*15934^4
604187^4+20032*47601^4=669723^4+20032*36337^4
608314^4+20032*57227^4=769786^4+20032*13373^4
221079^4+20032*61036^4=510169^4+20032*57081^4
222712^4+20032*71363^4=421768^4+20032*70339^4
415427^4+20032*92448^4=547987^4+20032*91479^4
15798^4+20032*104027^4=601642^4+20032*102543^4

Found 52 solutions.
Search finished successfully.

real 67m56.087s
user 56m55.653s
sys 0m41.256s

-bash-3.1$ time ./dqde4 20033 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20033, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 192939389
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
466^4+20033*53^4=673^4+20033*8^4
1171^4+20033*226^4=2712^4+20033*39^4
4364^4+20033*319^4=4882^4+20033*101^4
21167^4+20033*1135^4=21981^4+20033*405^4
9721^4+20033*1162^4=13808^4+20033*821^4
2763^4+20033*1167^4=10669^4+20033*1049^4
5803^4+20033*1288^4=15049^4+20033*706^4
527^4+20033*2104^4=12721^4+20033*2068^4
22279^4+20033*2411^4=30989^4+20033*481^4
2839^4+20033*2432^4=28852^4+20033*793^4
15427^4+20033*2852^4=34287^4+20033*18^4
41053^4+20033*3308^4=47217^4+20033*1914^4
24452^4+20033*3527^4=27942^4+20033*3453^4
61868^4+20033*4009^4=66169^4+20033*2392^4
25448^4+20033*5237^4=61561^4+20033*2738^4
21352^4+20033*6593^4=75823^4+20033*3976^4
9017^4+20033*7522^4=61478^4+20033*7063^4
59057^4+20033*8434^4=103217^4+20033*1058^4
71597^4+20033*8543^4=107293^4+20033*2191^4
90721^4+20033*9952^4=127498^4+20033*181^4
120922^4+20033*15173^4=187922^4+20033*6139^4
86784^4+20033*16113^4=193678^4+20033*533^4
94428^4+20033*18087^4=165314^4+20033*16477^4
37462^4+20033*18667^4=221761^4+20033*5312^4
251557^4+20033*19114^4=285861^4+20033*2538^4
135888^4+20033*21339^4=217001^4+20033*18362^4
120603^4+20033*21987^4=260231^4+20033*11129^4
93136^4+20033*22211^4=254003^4+20033*14084^4
935384^4+20033*23201^4=937132^4+20033*7583^4
377852^4+20033*23459^4=386093^4+20033*21436^4
102561^4+20033*24613^4=293913^4+20033*1933^4
96481^4+20033*27314^4=231821^4+20033*25408^4
388067^4+20033*27614^4=416542^4+20033*21427^4
228791^4+20033*29187^4=337331^4+20033*21561^4
72261^4+20033*33576^4=329273^4+20033*28774^4
349457^4+20033*35393^4=442617^4+20033*25113^4
101889^4+20033*37243^4=260313^4+20033*36109^4
242566^4+20033*38317^4=401036^4+20033*31913^4
79041^4+20033*38452^4=414309^4+20033*29102^4
470633^4+20033*44359^4=593729^4+20033*18527^4
561102^4+20033*49927^4=580779^4+20033*48388^4
517236^4+20033*50373^4=528299^4+20033*49744^4
450219^4+20033*60558^4=711787^4+20033*40486^4
580699^4+20033*72932^4=908242^4+20033*6263^4
90581^4+20033*84718^4=677909^4+20033*80006^4
187227^4+20033*92468^4=640281^4+20033*89714^4
689309^4+20033*124916^4=911857^4+20033*121822^4
405839^4+20033*200882^4=623388^4+20033*200691^4

Found 48 solutions.
Search finished successfully.

real 56m55.278s
user 55m28.426s
sys 0m26.085s

-bash-3.1$ time ./dqde4 20034 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20034, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 220129538
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
4143^4+20034*376^4=5097^4+20034*178^4
1293^4+20034*529^4=5427^4+20034*433^4
5580^4+20034*785^4=6852^4+20034*751^4
14169^4+20034*851^4=15009^4+20034*239^4
8341^4+20034*1207^4=14717^4+20034*387^4
3833^4+20034*1396^4=13177^4+20034*1232^4
3909^4+20034*1451^4=14403^4+20034*1231^4
3309^4+20034*1864^4=20883^4+20034*1268^4
11049^4+20034*2738^4=30447^4+20034*1936^4
21387^4+20034*3517^4=32517^4+20034*3221^4
19824^4+20034*5527^4=33012^4+20034*5449^4
2151^4+20034*5666^4=35481^4+20034*5554^4
477^4+20034*5887^4=69483^4+20034*2477^4
55023^4+20034*6092^4=65937^4+20034*5464^4
125719^4+20034*9021^4=139705^4+20034*2965^4
62001^4+20034*9751^4=69753^4+20034*9629^4
129931^4+20034*10247^4=149965^4+20034*1515^4
5648^4+20034*10583^4=125852^4+20034*2167^4
120292^4+20034*14589^4=179476^4+20034*7933^4
110829^4+20034*16114^4=112275^4+20034*16090^4
14559^4+20034*17015^4=79113^4+20034*16915^4
93901^4+20034*17632^4=181499^4+20034*14674^4
52207^4+20034*27358^4=151481^4+20034*27036^4
29747^4+20034*27593^4=210661^4+20034*26341^4
423921^4+20034*31646^4=476391^4+20034*14488^4
366924^4+20034*33653^4=457452^4+20034*6283^4
309917^4+20034*34236^4=414763^4+20034*24446^4
271337^4+20034*34572^4=417217^4+20034*20786^4
34199^4+20034*36156^4=217367^4+20034*35552^4
346641^4+20034*36437^4=439137^4+20034*28141^4
481023^4+20034*42769^4=578967^4+20034*25301^4
294033^4+20034*42998^4=394809^4+20034*40072^4
2441^4+20034*44002^4=358031^4+20034*41368^4
188947^4+20034*45077^4=464075^4+20034*37015^4
145461^4+20034*45488^4=469293^4+20034*37042^4
570801^4+20034*54947^4=732879^4+20034*10909^4
57693^4+20034*55591^4=645357^4+20034*30737^4
172773^4+20034*80531^4=745611^4+20034*71867^4
480222^4+20034*81941^4=841098^4+20034*69067^4
383146^4+20034*118393^4=859718^4+20034*114233^4
519153^4+20034*121780^4=774153^4+20034*119750^4
710607^4+20034*203476^4=864201^4+20034*203026^4

Found 42 solutions.
Search finished successfully.

real 76m8.657s
user 55m39.766s
sys 1m6.029s

-bash-3.1$ time ./dqde4 20035 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20035, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 29012320
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
47122^4+20035*2777^4=49046^4+20035*2023^4
32555^4+20035*9699^4=112695^4+20035*5407^4
861711^4+20035*37838^4=877327^4+20035*18^4
22424^4+20035*51263^4=602668^4+20035*23809^4

Found 4 solutions.
Search finished successfully.

real 43m5.245s
user 43m3.019s
sys 0m2.212s

(続く)

-bash-3.1$ time ./dqde4 20036 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20036, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 57789082
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1009^4+20036*249^4=2879^4+20036*147^4
265^4+20036*263^4=2583^4+20036*225^4
25474^4+20036*1073^4=25862^4+20036*353^4
26188^4+20036*2033^4=30024^4+20036*129^4
19423^4+20036*2426^4=30241^4+20036*22^4
13019^4+20036*7639^4=63109^4+20036*7151^4
81894^4+20036*11623^4=142002^4+20036*3767^4
109973^4+20036*13295^4=140027^4+20036*11795^4
255539^4+20036*14158^4=262429^4+20036*11296^4
126471^4+20036*14532^4=184087^4+20036*2642^4
370393^4+20036*16542^4=377561^4+20036*2178^4
18344^4+20036*27927^4=202052^4+20036*26919^4
492623^4+20036*39268^4=537679^4+20036*32716^4
769635^4+20036*57654^4=863645^4+20036*29846^4
275111^4+20036*66992^4=799833^4+20036*5964^4
102761^4+20036*77351^4=920313^4+20036*1347^4

Found 16 solutions.
Search finished successfully.

real 42m16.744s
user 42m12.888s
sys 0m3.813s

-bash-3.1$ time ./dqde4 20037 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20037, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 21533023
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
269517^4+20037*79499^4=910701^4+20037*49237^4
404557^4+20037*148968^4=811021^4+20037*147412^4

Found 2 solutions.
Search finished successfully.

real 54m57.099s
user 54m54.737s
sys 0m2.282s

-bash-3.1$ time ./dqde4 20038 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20038, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 58977235
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
8104^4+20038*373^4=8276^4+20038*149^4
23857^4+20038*699^4=23943^4+20038*257^4
38755^4+20038*5316^4=61435^4+20038*3762^4
26491^4+20038*5347^4=63637^4+20038*2203^4
34597^4+20038*8464^4=85939^4+20038*7058^4
183647^4+20038*22759^4=283751^4+20038*6269^4
143521^4+20038*23568^4=218711^4+20038*21546^4
132302^4+20038*35077^4=413798^4+20038*16027^4
214237^4+20038*49411^4=573523^4+20038*28571^4
407531^4+20038*51206^4=459091^4+20038*49564^4
459253^4+20038*66461^4=697877^4+20038*56083^4

Found 11 solutions.
Search finished successfully.

real 48m39.961s
user 48m36.943s
sys 0m2.975s

-bash-3.1$ time ./dqde4 20039 -m 200000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20039, N = 200000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 3786345
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2067^4+20039*86^4=2079^4+20039*76^4
8071^4+20039*974^4=12217^4+20039*86^4
19645^4+20039*1075^4=20433^4+20039*513^4
17396^4+20039*1957^4=22682^4+20039*1567^4
5897^4+20039*2102^4=23863^4+20039*1358^4
1917^4+20039*2136^4=25411^4+20039*316^4
40459^4+20039*3272^4=46607^4+20039*1894^4
12107^4+20039*4226^4=32117^4+20039*4042^4
379^4+20039*4697^4=16963^4+20039*4687^4
30878^4+20039*5791^4=69574^4+20039*929^4
112601^4+20039*11956^4=137541^4+20039*10146^4
105228^4+20039*12131^4=122802^4+20039*11321^4

Found 12 solutions.
Search finished successfully.

real 0m45.307s
user 0m45.042s
sys 0m0.260s

-bash-3.1$ time ./dqde4 20040 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20040, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 194911198
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
14377^4+20040*673^4=14711^4+20040*67^4
14738^4+20040*1387^4=18662^4+20040*227^4
29930^4+20040*7401^4=86710^4+20040*3849^4
9672^4+20040*9677^4=109872^4+20040*6221^4
34410^4+20040*9871^4=115890^4+20040*4871^4
14375^4+20040*12856^4=119225^4+20040*11458^4
219852^4+20040*21973^4=269952^4+20040*17059^4
152498^4+20040*38681^4=438014^4+20040*25591^4
90069^4+20040*50222^4=278667^4+20040*49624^4
279148^4+20040*61891^4=739552^4+20040*14843^4
592561^4+20040*170402^4=934577^4+20040*168766^4

Found 11 solutions.
Search finished successfully.

real 57m17.275s
user 54m9.622s
sys 0m29.724s

(続く)

-bash-3.1$ time ./dqde4 20041 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20041, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 74817518
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
77^4+20041*51^4=441^4+20041*47^4
1519^4+20041*512^4=6097^4+20041*76^4
3010^4+20041*989^4=10472^4+20041*775^4
11393^4+20041*1878^4=18253^4+20041*1668^4
34223^4+20041*5622^4=49693^4+20041*5256^4
72516^4+20041*9299^4=82904^4+20041*8979^4
28648^4+20041*9795^4=106460^4+20041*7293^4
16863^4+20041*11506^4=67949^4+20041*11328^4
695091^4+20041*14369^4=695679^4+20041*7501^4
81747^4+20041*19442^4=203629^4+20041*15606^4
174816^4+20041*19727^4=246454^4+20041*10869^4
194128^4+20041*23293^4=274292^4+20041*16963^4
659407^4+20041*65816^4=818251^4+20041*49138^4
800977^4+20041*128490^4=967773^4+20041*125660^4
268959^4+20041*353927^4=672233^4+20041*353871^4

Found 15 solutions.
Search finished successfully.

real 45m31.963s
user 45m26.475s
sys 0m5.474s

-bash-3.1$ time ./dqde4 20042 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20042, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 31869678
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
161179^4+20042*12017^4=181221^4+20042*5169^4
830679^4+20042*22443^4=832807^4+20042*9827^4
182313^4+20042*44532^4=530089^4+20042*14816^4

Found 3 solutions.
Search finished successfully.

real 34m27.409s
user 34m24.877s
sys 0m2.532s

-bash-3.1$ time ./dqde4 20043 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20043, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 115351745
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
34141^4+20043*1208^4=34403^4+20043*396^4
12578^4+20043*1809^4=17032^4+20043*1669^4
104642^4+20043*2359^4=104696^4+20043*2077^4
11633^4+20043*2391^4=28453^4+20043*973^4
80103^4+20043*4733^4=84171^4+20043*2681^4
60354^4+20043*5363^4=73716^4+20043*1999^4
64575^4+20043*8773^4=107805^4+20043*2689^4
145449^4+20043*29251^4=325443^4+20043*21007^4
592233^4+20043*34391^4=615027^4+20043*25117^4
102927^4+20043*35674^4=311217^4+20043*32798^4
191744^4+20043*48353^4=576622^4+20043*11587^4
833199^4+20043*59623^4=923511^4+20043*25009^4
66076^4+20043*67547^4=266402^4+20043*67343^4
252609^4+20043*105596^4=372867^4+20043*105434^4
161399^4+20043*124785^4=913601^4+20043*120055^4

Found 15 solutions.
Search finished successfully.

real 49m25.759s
user 49m15.322s
sys 0m10.437s

-bash-3.1$ time ./dqde4 20044 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20044, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 36914900
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
392709^4+20044*51586^4=563083^4+20044*42468^4

Found 1 solutions.
Search finished successfully.

real 54m54.564s
user 54m51.326s
sys 0m3.082s

-bash-3.1$ time ./dqde4 20045 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20045, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 56772426
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
23931^4+20045*959^4=24177^4+20045*635^4
7868^4+20045*14561^4=112824^4+20045*13857^4
176265^4+20045*19398^4=248005^4+20045*5648^4
19753^4+20045*41750^4=156059^4+20045*41648^4
376319^4+20045*46808^4=579723^4+20045*20190^4
353177^4+20045*63563^4=604689^4+20045*56829^4
506465^4+20045*73102^4=535875^4+20045*72564^4
18687^4+20045*74081^4=620037^4+20045*69059^4

Found 8 solutions.
Search finished successfully.

real 41m9.023s
user 41m4.180s
sys 0m4.543s

(続く)

-bash-3.1$ time ./dqde4 20046 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20046, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 277372425
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
541^4+20046*87^4=853^4+20046*77^4
1603^4+20046*326^4=3907^4+20046*22^4
203^4+20046*483^4=3691^4+20046*461^4
13011^4+20046*2372^4=28533^4+20046*382^4
19423^4+20046*2504^4=30217^4+20046*1482^4
25553^4+20046*4566^4=54959^4+20046*946^4
43736^4+20046*4743^4=59156^4+20046*2969^4
80836^4+20046*5831^4=90088^4+20046*743^4
148997^4+20046*6896^4=151693^4+20046*4562^4
22913^4+20046*7391^4=83399^4+20046*4917^4
13778^4+20046*7927^4=94162^4+20046*2313^4
2183^4+20046*8964^4=106631^4+20046*1652^4
63164^4+20046*16623^4=198304^4+20046*1551^4
163244^4+20046*21747^4=265432^4+20046*10349^4
155923^4+20046*22057^4=267613^4+20046*10079^4
442777^4+20046*23799^4=449009^4+20046*21421^4
142499^4+20046*23876^4=274853^4+20046*15706^4
203191^4+20046*25527^4=317903^4+20046*3467^4
77522^4+20046*25639^4=305386^4+20046*2553^4
89813^4+20046*25699^4=144827^4+20046*25419^4
990797^4+20046*28093^4=993757^4+20046*14629^4
190709^4+20046*29177^4=241597^4+20046*28069^4
55009^4+20046*37043^4=435439^4+20046*17317^4
537343^4+20046*37933^4=593737^4+20046*13159^4
30461^4+20046*40751^4=484837^4+20046*6003^4
88176^4+20046*45097^4=535356^4+20046*14263^4
349005^4+20046*49634^4=607821^4+20046*3950^4
492563^4+20046*51919^4=576091^4+20046*46581^4
339823^4+20046*55618^4=673007^4+20046*1914^4
166786^4+20046*56107^4=433414^4+20046*53493^4
388421^4+20046*66807^4=788771^4+20046*36349^4
250064^4+20046*67781^4=808268^4+20046*10341^4
431114^4+20046*72689^4=876238^4+20046*21969^4
119717^4+20046*76827^4=459979^4+20046*75571^4

Found 34 solutions.
Search finished successfully.

real 100m31.611s
user 54m18.508s
sys 1m7.735s

-bash-3.1$ time ./dqde4 20047 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20047, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 33420435
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
9138^4+20047*2018^4=10909^4+20047*2007^4
80813^4+20047*9611^4=120907^4+20047*317^4

Found 2 solutions.
Search finished successfully.

real 39m49.833s
user 39m47.459s
sys 0m2.342s

-bash-3.1$ time ./dqde4 20048 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20048, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 153126989
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2331^4+20048*696^4=4837^4+20048*676^4
7156^4+20048*709^4=9312^4+20048*303^4
1544^4+20048*827^4=3692^4+20048*823^4
8272^4+20048*923^4=11776^4+20048*101^4
14146^4+20048*1067^4=14862^4+20048*963^4
7332^4+20048*1251^4=14864^4+20048*631^4
53861^4+20048*3133^4=56367^4+20048*1884^4
21236^4+20048*5249^4=42488^4+20048*4963^4
37846^4+20048*6443^4=57382^4+20048*5987^4
61339^4+20048*7300^4=87589^4+20048*4970^4
8396^4+20048*7663^4=16664^4+20048*7661^4
236293^4+20048*8278^4=238057^4+20048*353^4
204756^4+20048*15261^4=230572^4+20048*5533^4
169022^4+20048*16291^4=204106^4+20048*12521^4
669142^4+20048*21431^4=672642^4+20048*2931^4
54269^4+20048*24598^4=186307^4+20048*23528^4
149393^4+20048*29017^4=244049^4+20048*27317^4
8906^4+20048*30133^4=353302^4+20048*14747^4
80816^4+20048*30427^4=240668^4+20048*28841^4
729596^4+20048*44059^4=774004^4+20048*2213^4
788497^4+20048*55246^4=870117^4+20048*8301^4
232808^4+20048*60367^4=718972^4+20048*17701^4
745293^4+20048*104754^4=986227^4+20048*97024^4

Found 23 solutions.
Search finished successfully.

real 46m9.235s
user 45m55.336s
sys 0m13.899s

-bash-3.1$ time ./dqde4 20049 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20049, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 252868906
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
49^4+20049*24^4=277^4+20049*14^4
1864^4+20049*229^4=2863^4+20049*32^4
303^4+20049*284^4=1164^4+20049*283^4
20203^4+20049*523^4=20221^4+20049*461^4
15384^4+20049*959^4=16401^4+20049*418^4
16065^4+20049*1180^4=18021^4+20049*154^4
28283^4+20049*2066^4=30239^4+20049*1704^4
3883^4+20049*3554^4=33386^4+20049*3143^4
78520^4+20049*3707^4=80405^4+20049*582^4
20757^4+20049*3974^4=39828^4+20049*3397^4
27734^4+20049*4313^4=44360^4+20049*3675^4
7361^4+20049*4441^4=52297^4+20049*2001^4
35343^4+20049*5102^4=60771^4+20049*2944^4
22900^4+20049*5165^4=61534^4+20049*1791^4
33713^4+20049*5966^4=49580^4+20049*5665^4
37491^4+20049*6956^4=62754^4+20049*6389^4
100706^4+20049*7057^4=110323^4+20049*3858^4
6382^4+20049*7439^4=48599^4+20049*7264^4
11513^4+20049*8858^4=105401^4+20049*1138^4
89951^4+20049*10408^4=131566^4+20049*2729^4
416267^4+20049*13262^4=417967^4+20049*8916^4
58862^4+20049*13963^4=166241^4+20049*4766^4
47221^4+20049*14241^4=153269^4+20049*10849^4
56984^4+20049*15677^4=186701^4+20049*4246^4
117679^4+20049*15734^4=194126^4+20049*2021^4
94179^4+20049*24164^4=271197^4+20049*16552^4
232651^4+20049*26072^4=294328^4+20049*21991^4
47536^4+20049*27051^4=87634^4+20049*27017^4
189486^4+20049*27137^4=331788^4+20049*6829^4
105568^4+20049*27661^4=306058^4+20049*19809^4
183059^4+20049*30436^4=360403^4+20049*16416^4
297344^4+20049*32791^4=403783^4+20049*21662^4
116722^4+20049*36007^4=426068^4+20049*14683^4
536553^4+20049*36211^4=581541^4+20049*19633^4
522727^4+20049*44464^4=612214^4+20049*28127^4
88652^4+20049*45431^4=362981^4+20049*42932^4
622642^4+20049*47341^4=702023^4+20049*25222^4
303676^4+20049*49781^4=589727^4+20049*27016^4
6187^4+20049*51254^4=588437^4+20049*30978^4
564966^4+20049*53017^4=714258^4+20049*4903^4
270993^4+20049*57080^4=660726^4+20049*34265^4
12374^4+20049*58933^4=700723^4+20049*13888^4
331613^4+20049*63344^4=463664^4+20049*61599^4
213228^4+20049*76073^4=834747^4+20049*55336^4
163934^4+20049*76163^4=811784^4+20049*58887^4
508317^4+20049*85609^4=640347^4+20049*83519^4
261773^4+20049*90988^4=619894^4+20049*88523^4
77202^4+20049*131561^4=770235^4+20049*129590^4
370717^4+20049*192404^4=645262^4+20049*192133^4

Found 49 solutions.
Search finished successfully.

real 72m15.630s
user 49m22.022s
sys 1m7.643s

-bash-3.1$ time ./dqde4 20050 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20050, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 112700857
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
655^4+20050*74^4=935^4+20050*32^4
367^4+20050*98^4=1169^4+20050*2^4
1234^4+20050*237^4=2838^4+20050*77^4
10523^4+20050*1195^4=15173^4+20050*293^4
8025^4+20050*1607^4=18145^4+20050*1101^4
13948^4+20050*2039^4=24548^4+20050*1015^4
2887^4+20050*2889^4=26863^4+20050*2571^4
32303^4+20050*3970^4=48071^4+20050*2456^4
1113^4+20050*4127^4=47809^4+20050*2331^4
242954^4+20050*7489^4=244046^4+20050*671^4
9708^4+20050*7619^4=52856^4+20050*7389^4
66167^4+20050*12450^4=128719^4+20050*10308^4
75131^4+20050*13001^4=156133^4+20050*4775^4
233768^4+20050*14775^4=249924^4+20050*6697^4
195893^4+20050*24493^4=302149^4+20050*11525^4
110397^4+20050*27514^4=328453^4+20050*2100^4
489445^4+20050*37421^4=555875^4+20050*15721^4
118240^4+20050*40901^4=474280^4+20050*23099^4
121135^4+20050*40974^4=403665^4+20050*35026^4
661915^4+20050*43614^4=717075^4+20050*8564^4
168859^4+20050*49263^4=431037^4+20050*45293^4
329412^4+20050*52813^4=638984^4+20050*15123^4
373565^4+20050*54333^4=646245^4+20050*31519^4
781972^4+20050*56233^4=856096^4+20050*36919^4
360303^4+20050*74099^4=886521^4+20050*20639^4
89825^4+20050*75298^4=836065^4+20050*52814^4
345869^4+20050*87196^4=987533^4+20050*57704^4
520997^4+20050*129700^4=739747^4+20050*128390^4

Found 28 solutions.
Search finished successfully.

real 43m2.965s
user 42m53.027s
sys 0m9.937s

(続く)

-bash-3.1$ time ./dqde4 20051 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20051, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 13397129
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
37811^4+20051*2869^4=42393^4+20051*1713^4
66024^4+20051*15629^4=174588^4+20051*10931^4
203464^4+20051*16531^4=237658^4+20051*5689^4

Found 3 solutions.
Search finished successfully.

real 24m35.974s
user 24m35.253s
sys 0m0.721s

-bash-3.1$ time ./dqde4 20052 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20052, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 65571602
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1466^4+20052*217^4=2546^4+20052*137^4
16469^4+20052*706^4=16741^4+20052*32^4
5927^4+20052*1599^4=11497^4+20052*1547^4
12742^4+20052*2549^4=30566^4+20052*53^4
74733^4+20052*6592^4=90861^4+20052*2588^4
129713^4+20052*8861^4=141809^4+20052*3277^4
193643^4+20052*9359^4=197371^4+20052*6781^4
109219^4+20052*9591^4=120893^4+20052*8369^4
114219^4+20052*11567^4=150981^4+20052*4669^4
4159^4+20052*13132^4=155663^4+20052*4626^4
99279^4+20052*15799^4=149409^4+20052*14341^4
528993^4+20052*37234^4=552399^4+20052*32984^4
115763^4+20052*42349^4=490253^4+20052*24227^4
106049^4+20052*57763^4=663167^4+20052*34957^4
587602^4+20052*64233^4=823798^4+20052*3033^4
644439^4+20052*71537^4=667833^4+20052*70619^4
594696^4+20052*122411^4=694956^4+20052*121669^4

Found 17 solutions.
Search finished successfully.

real 33m19.194s
user 33m13.810s
sys 0m5.384s

-bash-3.1$ time ./dqde4 20053 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20053, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 24713775
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
4739^4+20053*1456^4=15677^4+20053*1108^4
27613^4+20053*18069^4=209377^4+20053*10191^4
260747^4+20053*53639^4=585241^4+20053*40379^4
339798^4+20053*86017^4=702958^4+20053*81087^4

Found 4 solutions.
Search finished successfully.

real 30m37.904s
user 30m36.582s
sys 0m1.321s

-bash-3.1$ time ./dqde4 20054 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20054, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 75441836
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
66519^4+20054*18276^4=206897^4+20054*12062^4
20130^4+20054*18305^4=211998^4+20054*10369^4
190463^4+20054*27643^4=254519^4+20054*25759^4
5339^4+20054*67687^4=805331^4+20054*11189^4
7325^4+20054*73476^4=870715^4+20054*26382^4

Found 5 solutions.
Search finished successfully.

real 57m47.625s
user 57m39.678s
sys 0m7.875s

-bash-3.1$ time ./dqde4 20055 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20055, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 144609638
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
17344^4+20055*4339^4=39118^4+20055*3945^4
24971^4+20055*17925^4=193051^4+20055*13579^4
693378^4+20055*19891^4=694428^4+20055*17153^4
314623^4+20055*25027^4=364573^4+20055*2167^4
24865^4+20055*27903^4=252155^4+20055*25221^4
237821^4+20055*29087^4=363829^4+20055*6329^4
43744^4+20055*47989^4=135806^4+20055*47951^4
58243^4+20055*53270^4=633917^4+20055*5646^4
395125^4+20055*60894^4=675895^4+20055*46208^4
795448^4+20055*100669^4=991414^4+20055*92903^4

Found 10 solutions.
Search finished successfully.

real 48m2.534s
user 47m50.384s
sys 0m12.138s

(続く)

-bash-3.1$ time ./dqde4 20056 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20056, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 241705138
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1628^4+20056*233^4=2732^4+20056*151^4
18923^4+20056*1367^4=20821^4+20056*847^4
4176^4+20056*1747^4=19652^4+20056*1173^4
28762^4+20056*2709^4=36214^4+20056*1221^4
11720^4+20056*5237^4=62320^4+20056*1013^4
34786^4+20056*5273^4=63562^4+20056*2383^4
54523^4+20056*6220^4=78811^4+20056*1930^4
47616^4+20056*8971^4=107784^4+20056*1397^4
24094^4+20056*9977^4=85294^4+20056*9239^4
9818^4+20056*16067^4=170266^4+20056*12541^4
178266^4+20056*17473^4=203442^4+20056*15529^4
334044^4+20056*17717^4=346556^4+20056*3531^4
202534^4+20056*20095^4=264910^4+20056*6121^4
326249^4+20056*21583^4=353527^4+20056*7421^4
158771^4+20056*22108^4=271379^4+20056*3442^4
113038^4+20056*22891^4=274406^4+20056*1843^4
316364^4+20056*28707^4=367104^4+20056*22859^4
372987^4+20056*32879^4=454821^4+20056*1613^4
131401^4+20056*38975^4=263785^4+20056*37981^4
340658^4+20056*41199^4=391202^4+20056*39297^4
383242^4+20056*44029^4=519646^4+20056*33083^4
221496^4+20056*48281^4=577708^4+20056*2529^4
148747^4+20056*52012^4=502763^4+20056*45154^4
40676^4+20056*62409^4=435264^4+20056*60481^4
113657^4+20056*64212^4=172647^4+20056*64178^4
504185^4+20056*87649^4=540985^4+20056*87257^4

Found 26 solutions.
Search finished successfully.

real 69m44.649s
user 47m36.455s
sys 1m0.381s

-bash-3.1$ time ./dqde4 20057 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20057, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 29151364
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
45779^4+20057*6272^4=77151^4+20057*306^4
13061^4+20057*7202^4=36353^4+20057*7144^4
22932^4+20057*8397^4=99998^4+20057*191^4
126241^4+20057*8818^4=139181^4+20057*256^4
17429^4+20057*11467^4=62799^4+20057*11337^4
56413^4+20057*25148^4=296849^4+20057*10742^4
167864^4+20057*37259^4=444198^4+20057*12663^4
5329^4+20057*63572^4=727381^4+20057*39262^4

Found 8 solutions.
Search finished successfully.

real 38m51.117s
user 38m48.942s
sys 0m2.162s

-bash-3.1$ time ./dqde4 20058 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20058, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 15281394
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
168537^4+20058*7886^4=172449^4+20058*916^4
72731^4+20058*21756^4=152963^4+20058*21098^4

Found 2 solutions.
Search finished successfully.

real 30m4.575s
user 30m3.456s
sys 0m0.971s

-bash-3.1$ time ./dqde4 20059 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20059, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 93424099
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
3181^4+20059*5023^4=36937^4+20059*4829^4
53529^4+20059*12307^4=147061^4+20059*2391^4
44468^4+20059*14141^4=168466^4+20059*2281^4
146265^4+20059*20920^4=251189^4+20059*11226^4
110554^4+20059*21287^4=255596^4+20059*1837^4
592727^4+20059*22207^4=598469^4+20059*5971^4
12669^4+20059*23446^4=212609^4+20059*21156^4
118562^4+20059*27231^4=319152^4+20059*14357^4
340407^4+20059*40268^4=397147^4+20059*37878^4
100569^4+20059*62101^4=269751^4+20059*61829^4
511093^4+20059*65166^4=772683^4+20059*43754^4

Found 11 solutions.
Search finished successfully.

real 47m35.851s
user 47m27.924s
sys 0m7.895s

-bash-3.1$ time ./dqde4 20060 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20060, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 230399827
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
589^4+20060*57^4=707^4+20060*45^4
2051^4+20060*647^4=5501^4+20060*601^4
4113^4+20060*744^4=8159^4+20060*562^4
16331^4+20060*1657^4=20933^4+20060*1109^4
22251^4+20060*3183^4=38299^4+20060*1661^4
4596^4+20060*7991^4=78228^4+20060*6857^4
42637^4+20060*9710^4=114499^4+20060*4696^4
69096^4+20060*10833^4=131504^4+20060*337^4
606802^4+20060*25711^4=614498^4+20060*17201^4
101365^4+20060*55279^4=353525^4+20060*54097^4
327331^4+20060*62191^4=718147^4+20060*38825^4
264725^4+20060*71317^4=593355^4+20060*66819^4
153314^4+20060*72931^4=824498^4+20060*47939^4
95969^4+20060*112615^4=705487^4+20060*110389^4

Found 14 solutions.
Search finished successfully.

real 69m46.172s
user 48m34.841s
sys 0m58.314s

(続く)

-bash-3.1$ time ./dqde4 20061 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20061, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 107432217
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2064^4+20061*173^4=2394^4+20061*113^4
633^4+20061*1177^4=14007^4+20061*137^4
14238^4+20061*1427^4=18696^4+20061*569^4
1092^4+20061*1783^4=21198^4+20061*451^4
43098^4+20061*2701^4=46062^4+20061*947^4
25227^4+20061*4937^4=56433^4+20061*3229^4
89229^4+20061*6163^4=98007^4+20061*1361^4
39558^4+20061*7079^4=80808^4+20061*4747^4
56124^4+20061*7999^4=95448^4+20061*4609^4
22149^4+20061*11459^4=111309^4+20061*9899^4
14553^4+20061*11719^4=139377^4+20061*2687^4
105663^4+20061*14194^4=135069^4+20061*13184^4
58428^4+20061*15377^4=183252^4+20061*4079^4
118302^4+20061*16351^4=198546^4+20061*7841^4
26505^4+20061*33709^4=383631^4+20061*21445^4
124158^4+20061*35977^4=427302^4+20061*12617^4
35523^4+20061*37220^4=437025^4+20061*17822^4
522439^4+20061*37425^4=562561^4+20061*28745^4
556739^4+20061*74646^4=920809^4+20061*2812^4
110154^4+20061*108761^4=500592^4+20061*108149^4

Found 20 solutions.
Search finished successfully.

real 51m17.812s
user 51m7.916s
sys 0m9.877s

-bash-3.1$ time ./dqde4 20062 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20062, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 34601350
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1137^4+20062*181^4=1369^4+20062*177^4
11917^4+20062*1249^4=13877^4+20062*1123^4
66284^4+20062*2269^4=66536^4+20062*1853^4
49151^4+20062*3269^4=53393^4+20062*269^4
26219^4+20062*4478^4=54029^4+20062*976^4
75677^4+20062*10028^4=120547^4+20062*5912^4
90613^4+20062*12441^4=152997^4+20062*1457^4
80774^4+20062*13081^4=156122^4+20062*6503^4
24698^4+20062*13501^4=50818^4+20062*13469^4
87551^4+20062*14133^4=161649^4+20062*9683^4
72329^4+20062*18119^4=171281^4+20062*16043^4
124112^4+20062*22199^4=267356^4+20062*617^4
115067^4+20062*29111^4=347507^4+20062*1099^4
52709^4+20062*32681^4=388333^4+20062*9323^4
144153^4+20062*34844^4=416103^4+20062*6008^4
432703^4+20062*39674^4=492889^4+20062*33656^4
414887^4+20062*46498^4=572239^4+20062*29968^4
636730^4+20062*52017^4=746890^4+20062*7281^4
126471^4+20062*93214^4=492679^4+20062*92298^4

Found 19 solutions.
Search finished successfully.

real 43m59.106s
user 43m56.490s
sys 0m2.592s

-bash-3.1$ time ./dqde4 20063 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20063, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 29644256
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
29558^4+20063*7864^4=30631^4+20063*7861^4
38673^4+20063*14413^4=98862^4+20063*14008^4
389023^4+20063*15203^4=393434^4+20063*5248^4
71717^4+20063*26486^4=312473^4+20063*11624^4
35794^4+20063*42508^4=505907^4+20063*2663^4
845266^4+20063*46794^4=860089^4+20063*41487^4
457022^4+20063*48274^4=606317^4+20063*30533^4
607586^4+20063*75779^4=756698^4+20063*69571^4
40101^4+20063*501639^4=782432^4+20063*501602^4

Found 9 solutions.
Search finished successfully.

real 38m23.189s
user 38m20.945s
sys 0m2.202s

-bash-3.1$ time ./dqde4 20064 -m 200000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20064, N = 200000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 16885492
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2852^4+20064*429^4=3836^4+20064*403^4
2620^4+20064*477^4=5740^4+20064*61^4
2202^4+20064*1051^4=12234^4+20064*569^4
2817^4+20064*1138^4=9087^4+20064*1076^4
16327^4+20064*1448^4=19583^4+20064*883^4
2724^4+20064*1723^4=20508^4+20064*59^4
478^4+20064*1867^4=20498^4+20064*1353^4
55349^4+20064*1902^4=55459^4+20064*1749^4
3462^4+20064*2713^4=22074^4+20064*2551^4
26234^4+20064*3395^4=36266^4+20064*2895^4
7358^4+20064*3659^4=30766^4+20064*3407^4
54944^4+20064*5219^4=69992^4+20064*67^4
17159^4+20064*5222^4=33727^4+20064*5113^4
8858^4+20064*5901^4=68054^4+20064*3463^4
156792^4+20064*6709^4=159216^4+20064*3307^4
152898^4+20064*8159^4=158094^4+20064*4811^4
21173^4+20064*9346^4=111157^4+20064*2352^4
62974^4+20064*9381^4=100882^4+20064*7617^4
51803^4+20064*9544^4=114085^4+20064*3820^4
32817^4+20064*10696^4=124359^4+20064*5917^4
73903^4+20064*11026^4=108839^4+20064*9813^4
119027^4+20064*12708^4=150773^4+20064*10081^4
10256^4+20064*13613^4=99488^4+20064*13101^4
20567^4+20064*15472^4=84521^4+20064*15298^4
32548^4+20064*18043^4=96196^4+20064*17861^4
127832^4+20064*20913^4=164768^4+20064*20241^4
144446^4+20064*27373^4=151058^4+20064*27321^4
86204^4+20064*27437^4=164332^4+20064*27021^4

Found 28 solutions.
Search finished successfully.

real 1m5.790s
user 1m4.637s
sys 0m1.151s

-bash-3.1$ time ./dqde4 20065 -m 200000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20065, N = 200000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 7419492
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2823^4+20065*907^4=9071^4+20065*765^4
2894^4+20065*1275^4=12128^4+20065*1119^4
8933^4+20065*1942^4=20069^4+20065*1594^4
149721^4+20065*6782^4=152754^4+20065*2209^4
87879^4+20065*8381^4=105353^4+20065*6483^4
95279^4+20065*15278^4=117908^4+20065*14875^4
131061^4+20065*19172^4=141648^4+20065*18979^4
102936^4+20065*23681^4=147079^4+20065*23340^4

Found 8 solutions.
Search finished successfully.

real 1m3.816s
user 1m3.166s
sys 0m0.651s

(続く)

-bash-3.1$ time ./dqde4 20066 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20066, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 37913961
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
27311^4+20066*4649^4=32887^4+20066*4571^4
27799^4+20066*12962^4=112663^4+20066*11926^4
182546^4+20066*27663^4=336122^4+20066*8337^4
52159^4+20066*48659^4=212687^4+20066*48437^4

Found 4 solutions.
Search finished successfully.

real 33m24.044s
user 33m21.771s
sys 0m2.272s

-bash-3.1$ time ./dqde4 20067 -m 500000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20067, N = 500000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 10758581
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
6587^4+20067*441^4=7169^4+20067*53^4
2039^4+20067*763^4=6841^4+20067*693^4
4227^4+20067*1612^4=16701^4+20067*1304^4
17842^4+20067*7609^4=89182^4+20067*3783^4
271687^4+20067*12048^4=276811^4+20067*274^4
80963^4+20067*34052^4=92951^4+20067*34042^4

Found 6 solutions.
Search finished successfully.

real 6m46.721s
user 6m45.942s
sys 0m0.751s

-bash-3.1$ time ./dqde4 20068 -m 200000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20068, N = 200000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 4318324
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
509^4+20068*101^4=973^4+20068*89^4
3214^4+20068*643^4=7654^4+20068*269^4
1878^4+20068*1489^4=17722^4+20068*177^4
13907^4+20068*1719^4=19789^4+20068*1311^4
24474^4+20068*2297^4=30542^4+20068*1239^4
96797^4+20068*4998^4=100077^4+20068*692^4
35590^4+20068*8101^4=70550^4+20068*7493^4
67833^4+20068*9944^4=119913^4+20068*4798^4
158292^4+20068*10273^4=170748^4+20068*2849^4
158803^4+20068*11303^4=175757^4+20068*4639^4
41776^4+20068*12931^4=138812^4+20068*9901^4
2512^4+20068*13675^4=162184^4+20068*4715^4

Found 12 solutions.
Search finished successfully.

real 0m39.451s
user 0m39.157s
sys 0m0.290s

-bash-3.1$ time ./dqde4 20069 -m 500000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20069, N = 500000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 24955065
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
2663^4+20069*311^4=3917^4+20069*107^4
9858^4+20069*1441^4=13806^4+20069*1313^4
3061^4+20069*1844^4=21849^4+20069*678^4
14016^4+20069*2703^4=26686^4+20069*2341^4
82504^4+20069*3109^4=83218^4+20069*1879^4
24708^4+20069*6707^4=43038^4+20069*6577^4
222^4+20069*6777^4=35968^4+20069*6709^4
42516^4+20069*14277^4=170018^4+20069*2953^4
46505^4+20069*57224^4=474205^4+20069*53518^4
296027^4+20069*71749^4=311349^4+20069*71691^4

Found 10 solutions.
Search finished successfully.

real 9m24.383s
user 9m22.337s
sys 0m2.012s

-bash-3.1$ time ./dqde4 20070 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20070, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 95249394
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
83731^4+20070*13033^4=145067^4+20070*9803^4
91596^4+20070*13271^4=121032^4+20070*12425^4
232996^4+20070*26845^4=298112^4+20070*22851^4
491219^4+20070*34169^4=534581^4+20070*21013^4
651005^4+20070*40569^4=688915^4+20070*25681^4
422851^4+20070*51297^4=640499^4+20070*19049^4
322113^4+20070*64084^4=679359^4+20070*51044^4
2502^4+20070*66313^4=695586^4+20070*52631^4
106257^4+20070*70318^4=734007^4+20070*56224^4
369709^4+20070*86742^4=914771^4+20070*68990^4

Found 10 solutions.
Search finished successfully.

real 42m7.799s
user 41m59.989s
sys 0m7.735s

(続く)

-bash-3.1$ time ./dqde4 20071 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20071, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 18898053
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
18503^4+20071*1566^4=21639^4+20071*982^4
198876^4+20071*17551^4=242686^4+20071*963^4

Found 2 solutions.
Search finished successfully.

real 35m43.430s
user 35m42.271s
sys 0m1.141s

-bash-3.1$ time ./dqde4 20072 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20072, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 2785321
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
94^4+20072*7^4=106^4+20072*1^4
173^4+20072*31^4=269^4+20072*29^4
171^4+20072*36^4=341^4+20072*32^4
3754^4+20072*229^4=3954^4+20072*147^4
604^4+20072*277^4=3256^4+20072*131^4
5666^4+20072*637^4=8114^4+20072*83^4
23268^4+20072*819^4=23416^4+20072*523^4
6108^4+20072*869^4=10104^4+20072*589^4
14188^4+20072*1343^4=18036^4+20072*63^4
9946^4+20072*1661^4=19982^4+20072*629^4
30336^4+20072*1879^4=32364^4+20072*97^4
7226^4+20072*2291^4=27298^4+20072*373^4
29481^4+20072*2589^4=35753^4+20072*1037^4
83496^4+20072*3273^4=84464^4+20072*841^4
16693^4+20072*3601^4=40821^4+20072*2409^4
18205^4+20072*3631^4=43555^4+20072*217^4
4058^4+20072*3641^4=9462^4+20072*3639^4
63514^4+20072*4787^4=71234^4+20072*2699^4
29398^4+20072*4799^4=54874^4+20072*3281^4
6178^4+20072*4987^4=54038^4+20072*3731^4
23496^4+20072*5151^4=51388^4+20072*4391^4
16452^4+20072*5197^4=24564^4+20072*5171^4
33487^4+20072*5798^4=69841^4+20072*1648^4
47344^4+20072*7141^4=72316^4+20072*6211^4
39666^4+20072*8063^4=67818^4+20072*7577^4
66904^4+20072*9901^4=96716^4+20072*8891^4

Found 26 solutions.
Search finished successfully.

real 0m10.691s
user 0m10.429s
sys 0m0.261s

-bash-3.1$ time ./dqde4 20073 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20073, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 27729615
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
47876^4+20073*4843^4=61258^4+20073*3241^4
18862^4+20073*5043^4=59008^4+20073*2647^4
61513^4+20073*17971^4=72307^4+20073*17943^4
116291^4+20073*20554^4=231641^4+20073*14496^4
126781^4+20073*36219^4=394421^4+20073*26957^4
638528^4+20073*89163^4=839258^4+20073*82697^4

Found 6 solutions.
Search finished successfully.

real 34m43.618s
user 34m41.967s
sys 0m1.651s

-bash-3.1$ time ./dqde4 20074 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20074, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 43803428
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
79529^4+20074*2500^4=79903^4+20074*1070^4
115291^4+20074*15912^4=195587^4+20074*1662^4
901109^4+20074*27884^4=905227^4+20074*52^4
442443^4+20074*46007^4=598243^4+20074*9549^4
568923^4+20074*52181^4=709627^4+20074*4581^4
679039^4+20074*214808^4=814343^4+20074*214522^4

Found 6 solutions.
Search finished successfully.

real 45m22.744s
user 45m20.413s
sys 0m2.332s

-bash-3.1$ time ./dqde4 20075 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20075, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 1495441
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
966^4+20075*123^4=1516^4+20075*55^4
11233^4+20075*695^4=11981^4+20075*59^4
9367^4+20075*1070^4=13469^4+20075*484^4
10528^4+20075*1211^4=15346^4+20075*47^4
16475^4+20075*1214^4=18505^4+20075*164^4
400^4+20075*1381^4=15910^4+20075*817^4
13506^4+20075*1705^4=19956^4+20075*1219^4
35540^4+20075*1829^4=36730^4+20075*79^4
3452^4+20075*1891^4=21514^4+20075*1207^4
2875^4+20075*2258^4=6615^4+20075*2256^4
8935^4+20075*2822^4=25165^4+20075*2572^4
20398^4+20075*3509^4=42236^4+20075*1145^4
20325^4+20075*3594^4=43255^4+20075*992^4
40439^4+20075*5963^4=72773^4+20075*817^4
21629^4+20075*6359^4=39003^4+20075*6255^4
10779^4+20075*8145^4=55747^4+20075*7913^4

Found 16 solutions.
Search finished successfully.

real 0m7.143s
user 0m7.032s
sys 0m0.110s

(続く)

-bash-3.1$ time ./dqde4 20076 -m 500000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20076, N = 500000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 28599474
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1135^4+20076*239^4=2689^4+20076*165^4
4579^4+20076*448^4=5459^4+20076*366^4
9924^4+20076*463^4=10152^4+20076*31^4
14317^4+20076*1604^4=20099^4+20076*874^4
8984^4+20076*1705^4=17588^4+20076*1415^4
102808^4+20076*5951^4=104644^4+20076*5393^4
26084^4+20076*7207^4=34144^4+20076*7177^4
51029^4+20076*9004^4=108389^4+20076*2442^4
16144^4+20076*11265^4=55340^4+20076*11183^4
380201^4+20076*14668^4=384121^4+20076*7206^4
106577^4+20076*15154^4=149119^4+20076*13632^4
124833^4+20076*21163^4=255327^4+20076*5611^4
368993^4+20076*32002^4=437393^4+20076*19652^4
347299^4+20076*34995^4=459565^4+20076*7143^4
37292^4+20076*46551^4=235168^4+20076*46169^4
108299^4+20076*63279^4=395099^4+20076*62053^4

Found 16 solutions.
Search finished successfully.

real 9m18.267s
user 9m16.588s
sys 0m1.661s

-bash-3.1$ time ./dqde4 20077 -m 500000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20077, N = 500000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 24632187
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
29^4+20077*3^4=39^4+20077*1^4
83^4+20077*107^4=1273^4+20077*23^4
8184^4+20077*641^4=9356^4+20077*321^4
8861^4+20077*764^4=10369^4+20077*518^4
12799^4+20077*1006^4=13183^4+20077*962^4
36246^4+20077*5009^4=61532^4+20077*1101^4
32723^4+20077*5037^4=57033^4+20077*3631^4
36316^4+20077*6337^4=68854^4+20077*4907^4
92453^4+20077*11751^4=146109^4+20077*1663^4
145121^4+20077*12000^4=171103^4+20077*3420^4
20541^4+20077*12451^4=141003^4+20077*8123^4
50257^4+20077*12799^4=131617^4+20077*10511^4
193903^4+20077*13527^4=213689^4+20077*2463^4
109313^4+20077*19611^4=236193^4+20077*1733^4
166331^4+20077*22221^4=216313^4+20077*20391^4
59438^4+20077*23419^4=278912^4+20077*433^4
308269^4+20077*63914^4=466777^4+20077*61996^4

Found 17 solutions.
Search finished successfully.

real 9m48.142s
user 9m46.310s
sys 0m1.831s

-bash-3.1$ time ./dqde4 20078 -m 3000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20078, N = 3000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 150901824
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...

Found 0 solutions.
Search finished successfully.

real 425m0.549s
user 424m46.821s
sys 0m13.369s

-bash-3.1$ time ./dqde4 20079 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20079, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 2470557
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
101^4+20079*7^4=106^4+20079*6^4
284^4+20079*36^4=445^4+20079*15^4
1429^4+20079*166^4=2027^4+20079*106^4
1509^4+20079*257^4=2061^4+20079*247^4
1681^4+20079*296^4=3517^4+20079*146^4
836^4+20079*608^4=7237^4+20079*89^4
12253^4+20079*1963^4=13001^4+20079*1953^4
3801^4+20079*1981^4=23466^4+20079*746^4
17499^4+20079*3013^4=36336^4+20079*718^4
88979^4+20079*3049^4=89501^4+20079*1881^4
37700^4+20079*3215^4=45152^4+20079*817^4
46701^4+20079*3572^4=52521^4+20079*2134^4
1272^4+20079*4004^4=46959^4+20079*1963^4
48149^4+20079*4073^4=56222^4+20079*2594^4
23894^4+20079*4841^4=57934^4+20079*1449^4
28181^4+20079*5794^4=69397^4+20079*1346^4
74252^4+20079*7092^4=91019^4+20079*5001^4
31898^4+20079*14740^4=64811^4+20079*14675^4

Found 18 solutions.
Search finished successfully.

real 0m10.783s
user 0m10.542s
sys 0m0.240s

-bash-3.1$ time ./dqde4 20080 -m 200000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20080, N = 200000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 10210817
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
334^4+20080*117^4=1338^4+20080*73^4
103^4+20080*118^4=1403^4+20080*31^4
52^4+20080*159^4=1056^4+20080*155^4
13046^4+20080*1291^4=17062^4+20080*35^4
14352^4+20080*2435^4=29412^4+20080*167^4
11212^4+20080*2705^4=32296^4+20080*619^4
9672^4+20080*3115^4=35776^4+20080*1899^4
33637^4+20080*3835^4=48697^4+20080*34^4
47599^4+20080*4096^4=54307^4+20080*3193^4
35613^4+20080*4868^4=39687^4+20080*4771^4
6808^4+20080*5801^4=69056^4+20080*407^4
41131^4+20080*8104^4=71317^4+20080*7502^4
78588^4+20080*8905^4=88628^4+20080*8457^4
50093^4+20080*10463^4=113057^4+20080*8032^4
22466^4+20080*10565^4=125122^4+20080*4037^4
99355^4+20080*15852^4=192225^4+20080*1273^4
111614^4+20080*16489^4=189586^4+20080*11471^4
65466^4+20080*17963^4=152814^4+20080*16705^4

Found 18 solutions.
Search finished successfully.

real 1m9.477s
user 1m8.671s
sys 0m0.790s

(続く)

-bash-3.1$ time ./dqde4 20081 -m 500000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20081, N = 500000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 24334130
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
7217^4+20081*1052^4=12821^4+20081*346^4
14258^4+20081*2585^4=28706^4+20081*1895^4
43302^4+20081*4419^4=57103^4+20081*2278^4
43063^4+20081*6905^4=83225^4+20081*2729^4
111682^4+20081*12007^4=120088^4+20081*11611^4
118511^4+20081*13324^4=162156^4+20081*9117^4
121621^4+20081*18574^4=181864^4+20081*16573^4
399775^4+20081*22051^4=413785^4+20081*14843^4
48408^4+20081*29871^4=307913^4+20081*24302^4
465732^4+20081*29903^4=498156^4+20081*16591^4
308002^4+20081*32119^4=389229^4+20081*24654^4
449154^4+20081*32945^4=485580^4+20081*25699^4
3919^4+20081*45274^4=477091^4+20081*35684^4

Found 13 solutions.
Search finished successfully.

real 8m19.114s
user 8m17.311s
sys 0m1.721s

-bash-3.1$ time ./dqde4 20082 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20082, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 24602000
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
48611^4+20082*31433^4=363229^4+20082*18199^4
165803^4+20082*46442^4=400093^4+20082*42984^4
183403^4+20082*49992^4=593101^4+20082*19362^4
59951^4+20082*55043^4=642329^4+20082*28959^4
461497^4+20082*123909^4=877303^4+20082*120163^4

Found 5 solutions.
Search finished successfully.

real 34m59.399s
user 34m57.294s
sys 0m1.901s

-bash-3.1$ time ./dqde4 20083 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20083, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 47028838
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
9587^4+20083*2731^4=32539^4+20083*691^4
166171^4+20083*4618^4=166633^4+20083*2356^4
20560^4+20083*6453^4=53430^4+20083*6047^4
88183^4+20083*6804^4=99963^4+20083*3674^4
55019^4+20083*12777^4=71217^4+20083*12677^4
61597^4+20083*15077^4=179701^4+20083*4643^4

Found 6 solutions.
Search finished successfully.

real 38m41.401s
user 38m37.789s
sys 0m3.132s

-bash-3.1$ time ./dqde4 20084 -m 200000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20084, N = 200000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 2235496
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
133^4+20084*44^4=523^4+20084*14^4
9170^4+20084*785^4=10914^4+20084*399^4
38592^4+20084*3897^4=39268^4+20084*3863^4
8511^4+20084*6582^4=78353^4+20084*848^4
46456^4+20084*11327^4=135264^4+20084*2241^4
79853^4+20084*12487^4=106019^4+20084*11899^4
41922^4+20084*13993^4=78582^4+20084*13831^4
135838^4+20084*16931^4=176006^4+20084*15053^4
78549^4+20084*24009^4=148843^4+20084*23591^4

Found 9 solutions.
Search finished successfully.

real 0m39.149s
user 0m38.954s
sys 0m0.190s

-bash-3.1$ time ./dqde4 20085 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20085, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 183327028
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
4^4+20085*17^4=202^4+20085*5^4
239^4+20085*177^4=2027^4+20085*109^4
6787^4+20085*1264^4=9281^4+20085*1230^4
20411^4+20085*4392^4=34007^4+20085*4210^4
725923^4+20085*20024^4=727777^4+20085*11738^4
185176^4+20085*22139^4=278324^4+20085*1723^4
176329^4+20085*23311^4=260171^4+20085*18427^4
49156^4+20085*23719^4=209992^4+20085*21657^4
377417^4+20085*47591^4=465379^4+20085*44165^4
42163^4+20085*70444^4=202637^4+20085*70384^4
125346^4+20085*71681^4=527046^4+20085*68927^4
481875^4+20085*170762^4=809415^4+20085*169816^4

Found 12 solutions.
Search finished successfully.

real 59m29.089s
user 42m30.744s
sys 0m37.382s

(続く)

-bash-3.1$ time ./dqde4 20086 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20086, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 38367367
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
28369^4+20086*6023^4=70367^4+20086*3361^4
71927^4+20086*7271^4=95401^4+20086*1367^4
74803^4+20086*8778^4=110619^4+20086*2536^4
95183^4+20086*18451^4=217063^4+20086*9863^4
227627^4+20086*29529^4=357771^4+20086*16727^4
465443^4+20086*53466^4=677259^4+20086*13568^4

Found 6 solutions.
Search finished successfully.

real 38m34.170s
user 38m31.713s
sys 0m2.362s

-bash-3.1$ time ./dqde4 20087 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20087, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 51418638
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
37279^4+20087*5326^4=65051^4+20087*1748^4
116777^4+20087*22574^4=237299^4+20087*18256^4
233057^4+20087*126623^4=375561^4+20087*126519^4
84512^4+20087*277679^4=612838^4+20087*277597^4

Found 4 solutions.
Search finished successfully.

real 42m35.108s
user 42m31.472s
sys 0m3.562s

-bash-3.1$ time ./dqde4 20088 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20088, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 3307512
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
84^4+20088*25^4=288^4+20088*15^4
231^4+20088*29^4=327^4+20088*23^4
444^4+20088*67^4=816^4+20088*11^4
522^4+20088*93^4=966^4+20088*77^4
633^4+20088*98^4=1191^4+20088*16^4
2958^4+20088*121^4=2994^4+20088*71^4
282^4+20088*173^4=1398^4+20088*163^4
4686^4+20088*763^4=9078^4+20088*397^4
18462^4+20088*835^4=18834^4+20088*275^4
17832^4+20088*2081^4=24204^4+20088*1609^4
69312^4+20088*2411^4=69816^4+20088*277^4
1584^4+20088*2923^4=12924^4+20088*2909^4
39642^4+20088*3091^4=45546^4+20088*61^4
79386^4+20088*3161^4=80202^4+20088*2039^4
34152^4+20088*3245^4=40848^4+20088*2515^4
14808^4+20088*3359^4=39876^4+20088*1399^4
14608^4+20088*3761^4=44416^4+20088*1713^4
30168^4+20088*5463^4=56208^4+20088*4567^4
6852^4+20088*5617^4=66804^4+20088*1423^4
28902^4+20088*5777^4=69306^4+20088*79^4
25879^4+20088*5971^4=58441^4+20088*5167^4
34638^4+20088*6667^4=80022^4+20088*1571^4
11007^4+20088*6767^4=74367^4+20088*4897^4
18969^4+20088*7928^4=72729^4+20088*7116^4
46758^4+20088*11863^4=87162^4+20088*11447^4
37884^4+20088*11957^4=75948^4+20088*11723^4
51774^4+20088*13151^4=96654^4+20088*12689^4

Found 27 solutions.
Search finished successfully.

real 0m12.365s
user 0m12.084s
sys 0m0.280s

-bash-3.1$ time ./dqde4 20089 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20089, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 43767935
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1259^4+20089*848^4=9961^4+20089*406^4
18587^4+20089*1449^4=20779^4+20089*1017^4
4721^4+20089*3881^4=44899^4+20089*2227^4
44149^4+20089*6076^4=60299^4+20089*5468^4
256803^4+20089*34588^4=426223^4+20089*8358^4
276321^4+20089*41198^4=322349^4+20089*40284^4
40619^4+20089*53561^4=635423^4+20089*18413^4
741955^4+20089*59530^4=862489^4+20089*17696^4
4507^4+20089*65306^4=722011^4+20089*46466^4
67681^4+20089*71685^4=738567^4+20089*58355^4

Found 10 solutions.
Search finished successfully.

real 30m9.949s
user 30m7.293s
sys 0m2.612s

-bash-3.1$ time ./dqde4 20090 -m 500000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20090, N = 500000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 70051318
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
547^4+20090*43^4=629^4+20090*17^4
97^4+20090*100^4=1177^4+20090*46^4
14^4+20090*195^4=2282^4+20090*99^4
23497^4+20090*2633^4=31729^4+20090*1891^4
5241^4+20090*2932^4=29937^4+20090*2414^4
19859^4+20090*4565^4=35931^4+20090*4353^4
10339^4+20090*7187^4=60277^4+20090*6697^4
43519^4+20090*9672^4=111559^4+20090*5910^4
13097^4+20090*10145^4=24577^4+20090*10141^4
34963^4+20090*11080^4=122131^4+20090*7988^4
106841^4+20090*11936^4=139559^4+20090*9428^4
60130^4+20090*12011^4=135030^4+20090*8373^4
158473^4+20090*12904^4=184961^4+20090*5422^4
123660^4+20090*13171^4=155640^4+20090*10579^4
162988^4+20090*14285^4=197708^4+20090*5171^4
141215^4+20090*17168^4=215015^4+20090*4082^4
282426^4+20090*17987^4=302418^4+20090*8419^4
80773^4+20090*18512^4=220829^4+20090*5870^4
226296^4+20090*18911^4=266196^4+20090*9601^4
43589^4+20090*22363^4=266077^4+20090*5311^4
66763^4+20090*23954^4=123357^4+20090*23760^4
299721^4+20090*24039^4=326671^4+20090*20269^4
358131^4+20090*26947^4=390981^4+20090*20681^4
83841^4+20090*28207^4=335991^4+20090*5813^4
141275^4+20090*89371^4=415675^4+20090*88853^4

Found 25 solutions.
Search finished successfully.

real 10m32.764s
user 10m27.720s
sys 0m5.044s

(続く)

-bash-3.1$ time ./dqde4 20091 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20091, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 2831972
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
13^4+20091*10^4=115^4+20091*6^4
1127^4+20091*129^4=1489^4+20091*103^4
942^4+20091*131^4=1608^4+20091*31^4
893^4+20091*237^4=2003^4+20091*221^4
1195^4+20091*281^4=3359^4+20091*5^4
2154^4+20091*673^4=7944^4+20091*299^4
808^4+20091*723^4=8474^4+20091*359^4
4786^4+20091*851^4=10216^4+20091*303^4
5633^4+20091*854^4=9899^4+20091*568^4
4354^4+20091*891^4=8878^4+20091*763^4
9803^4+20091*955^4=10325^4+20091*923^4
6149^4+20091*1138^4=13399^4+20091*616^4
10043^4+20091*1490^4=14075^4+20091*1366^4
23110^4+20091*1591^4=25324^4+20091*605^4
31526^4+20091*1667^4=32696^4+20091*289^4
5036^4+20091*1783^4=21242^4+20091*261^4
38331^4+20091*2672^4=42033^4+20091*1322^4
7611^4+20091*2737^4=32571^4+20091*719^4
11222^4+20091*3401^4=40544^4+20091*541^4
40333^4+20091*3429^4=48119^4+20091*1329^4
29051^4+20091*3536^4=39739^4+20091*2868^4
87963^4+20091*3841^4=89049^4+20091*2869^4
2609^4+20091*3911^4=45899^4+20091*1901^4
14102^4+20091*4563^4=54358^4+20091*979^4
21829^4+20091*4641^4=55277^4+20091*1801^4
28995^4+20091*5864^4=63747^4+20091*4460^4
28277^4+20091*6786^4=70283^4+20091*5534^4
36311^4+20091*7189^4=81151^4+20091*4947^4
29593^4+20091*31999^4=63793^4+20091*31993^4

Found 29 solutions.
Search finished successfully.

real 0m13.163s
user 0m12.893s
sys 0m0.270s

-bash-3.1$ time ./dqde4 20092 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20092, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 13692455
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
8176^4+20092*1209^4=11916^4+20092*1079^4

Found 1 solutions.
Search finished successfully.

real 30m8.029s
user 30m7.167s
sys 0m0.861s

-bash-3.1$ time ./dqde4 20093 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20093, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 33046853
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
190345^4+20093*13942^4=211515^4+20093*7692^4
170349^4+20093*70998^4=732953^4+20093*57704^4

Found 2 solutions.
Search finished successfully.

real 37m13.283s
user 37m11.325s
sys 0m1.951s

-bash-3.1$ time ./dqde4 20094 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20094, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 2385489
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
128^4+20094*77^4=916^4+20094*19^4
619^4+20094*109^4=1013^4+20094*99^4
419^4+20094*119^4=941^4+20094*113^4
3241^4+20094*247^4=3679^4+20094*99^4
7361^4+20094*302^4=7463^4+20094*84^4
12179^4+20094*687^4=12709^4+20094*373^4
3365^4+20094*965^4=7459^4+20094*921^4
33239^4+20094*1616^4=34135^4+20094*20^4
66799^4+20094*1877^4=67007^4+20094*339^4
9783^4+20094*1882^4=13857^4+20094*1828^4
48727^4+20094*2794^4=50561^4+20094*2008^4
61249^4+20094*3067^4=63095^4+20094*625^4
34287^4+20094*3533^4=46089^4+20094*401^4
4852^4+20094*4183^4=49804^4+20094*87^4
51283^4+20094*4871^4=65341^4+20094*383^4
32969^4+20094*9966^4=71713^4+20094*9632^4

Found 16 solutions.
Search finished successfully.

real 0m12.472s
user 0m12.251s
sys 0m0.220s

-bash-3.1$ time ./dqde4 20095 -m 500000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20095, N = 500000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 26122156
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
55229^4+20095*2949^4=57303^4+20095*1199^4
5167^4+20095*3377^4=37319^4+20095*2407^4
55149^4+20095*3511^4=59168^4+20095*1242^4
37776^4+20095*9604^4=94851^4+20095*8227^4
157628^4+20095*14890^4=200063^4+20095*3533^4
387131^4+20095*17592^4=395169^4+20095*1946^4
146189^4+20095*19080^4=183369^4+20095*17738^4
27349^4+20095*19915^4=193696^4+20095*17188^4
212387^4+20095*45020^4=438691^4+20095*39220^4

Found 9 solutions.
Search finished successfully.

real 9m10.397s
user 9m8.654s
sys 0m1.741s

(続く)

-bash-3.1$ time ./dqde4 20096 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20096, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 3134707
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
316^4+20096*85^4=940^4+20096*61^4
308^4+20096*1243^4=14612^4+20096*587^4
1708^4+20096*1295^4=14620^4+20096*857^4
124^4+20096*1363^4=16204^4+20096*379^4
16159^4+20096*1928^4=16193^4+20096*1927^4
3211^4+20096*2434^4=28331^4+20096*1321^4
17788^4+20096*2453^4=22548^4+20096*2307^4
41016^4+20096*3787^4=49776^4+20096*2531^4
4889^4+20096*5689^4=66119^4+20096*3134^4
24348^4+20096*6711^4=79612^4+20096*2617^4
60776^4+20096*7191^4=90584^4+20096*1257^4
68939^4+20096*7708^4=94027^4+20096*5258^4

Found 12 solutions.
Search finished successfully.

real 0m15.348s
user 0m15.117s
sys 0m0.230s

-bash-3.1$ time ./dqde4 20097 -m 100000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20097, N = 100000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 4801964
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
72^4+20097*7^4=93^4+20097*2^4
23^4+20097*11^4=131^4+20097*1^4
351^4+20097*26^4=384^4+20097*19^4
411^4+20097*136^4=807^4+20097*134^4
138^4+20097*157^4=1776^4+20097*103^4
3446^4+20097*229^4=3743^4+20097*8^4
1362^4+20097*257^4=1971^4+20097*248^4
449^4+20097*462^4=5293^4+20097*284^4
1154^4+20097*579^4=6887^4+20097*152^4
2323^4+20097*589^4=3709^4+20097*579^4
982^4+20097*591^4=7037^4+20097*72^4
3204^4+20097*719^4=7989^4+20097*514^4
4024^4+20097*863^4=10331^4+20097*174^4
694^4+20097*951^4=11276^4+20097*341^4
26731^4+20097*978^4=26938^4+20097*587^4
33923^4+20097*1154^4=33991^4+20097*1056^4
11994^4+20097*1499^4=18693^4+20097*238^4
8943^4+20097*1574^4=17853^4+20097*1088^4
34462^4+20097*1607^4=34651^4+20097*1504^4
679^4+20097*1823^4=21343^4+20097*921^4
2526^4+20097*1957^4=22917^4+20097*986^4
5228^4+20097*2091^4=24758^4+20097*823^4
39261^4+20097*2230^4=41127^4+20097*880^4
22237^4+20097*2297^4=27043^4+20097*1913^4
2150^4+20097*2397^4=28540^4+20097*103^4
8192^4+20097*2545^4=30319^4+20097*600^4
42516^4+20097*2669^4=45264^4+20097*1453^4
18119^4+20097*2842^4=29383^4+20097*2406^4
5521^4+20097*3144^4=35509^4+20097*2078^4
34614^4+20097*3349^4=44619^4+20097*262^4
37673^4+20097*3851^4=45989^4+20097*3143^4
86456^4+20097*4167^4=88598^4+20097*1987^4
70753^4+20097*4348^4=75316^4+20097*1343^4
11838^4+20097*5849^4=43833^4+20097*5606^4
6187^4+20097*6369^4=70141^4+20097*4583^4
72517^4+20097*7356^4=91976^4+20097*5221^4
14536^4+20097*7587^4=86993^4+20097*4646^4
12522^4+20097*7751^4=55686^4+20097*7481^4
40665^4+20097*7796^4=64605^4+20097*7378^4
61783^4+20097*8446^4=70517^4+20097*8228^4
23717^4+20097*12746^4=91519^4+20097*12304^4
64672^4+20097*16613^4=82046^4+20097*16537^4

Found 42 solutions.
Search finished successfully.

real 0m16.485s
user 0m16.124s
sys 0m0.360s

-bash-3.1$ time ./dqde4 20098 -m 200000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20098, N = 200000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 4996649
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
93^4+20098*8^4=107^4+20098*6^4
771^4+20098*329^4=3867^4+20098*157^4
1073^4+20098*359^4=3113^4+20098*331^4
7560^4+20098*641^4=7900^4+20098*609^4
4486^4+20098*717^4=7578^4+20098*589^4
4951^4+20098*853^4=9553^4+20098*617^4
1561^4+20098*2434^4=21761^4+20098*2212^4
76387^4+20098*6011^4=87803^4+20098*2551^4
28313^4+20098*10552^4=125711^4+20098*1354^4
5277^4+20098*11518^4=85669^4+20098*11052^4
47522^4+20098*11961^4=136298^4+20098*7719^4
33688^4+20098*12123^4=102708^4+20098*11269^4
77190^4+20098*15281^4=150650^4+20098*13233^4
90589^4+20098*16222^4=195421^4+20098*2426^4
104361^4+20098*20648^4=177023^4+20098*19302^4

Found 15 solutions.
Search finished successfully.

real 1m2.130s
user 1m1.699s
sys 0m0.432s

-bash-3.1$ time ./dqde4 20099 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20099, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 87114583
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
1185^4+20099*234^4=2795^4+20099*88^4
4079^4+20099*1445^4=9253^4+20099*1415^4
39909^4+20099*2331^4=40487^4+20099*2167^4
8759^4+20099*5516^4=65673^4+20099*864^4
285524^4+20099*14909^4=295556^4+20099*4547^4
18172^4+20099*16819^4=110906^4+20099*16409^4
71603^4+20099*19489^4=173963^4+20099*17783^4
109357^4+20099*19712^4=236903^4+20099*6098^4
225366^4+20099*25279^4=305964^4+20099*17813^4
293541^4+20099*27423^4=350423^4+20099*20731^4

Found 10 solutions.
Search finished successfully.

real 44m55.375s
user 44m47.614s
sys 0m7.755s

-bash-3.1$ time ./dqde4 20100 -m 1000000
--- Diophantine Equation A^4 + h*B^4 = C^4 + h*D^4 Search Started ---
Settings: h = 20100, N = 1000000, FILTER_MOD = 1360, HASH_MOD = 9999991, Verbose = OFF
[2/4] Computing and filtering (z^4 - x^4) / h...
Total nodes collected after filter: 139841863
[3/4] Creating hash index table...
[4/4] Generating y^4 - w^4 and performing main search...
799^4+20100*111^4=1201^4+20100*91^4
139^4+20100*303^4=3077^4+20100*251^4
8578^4+20100*755^4=10454^4+20100*99^4
25195^4+20100*1669^4=26395^4+20100*1383^4
6920^4+20100*1797^4=21220^4+20100*821^4
59290^4+20100*3401^4=61310^4+20100*2599^4
32755^4+20100*3652^4=45635^4+20100*2098^4
534634^4+20100*24187^4=545138^4+20100*10731^4
203425^4+20100*25508^4=316655^4+20100*9558^4
24214^4+20100*36369^4=88802^4+20100*36353^4
64648^4+20100*42321^4=500564^4+20100*17089^4
541424^4+20100*43547^4=630668^4+20100*5141^4
195487^4+20100*49252^4=588241^4+20100*402^4
218163^4+20100*56942^4=646941^4+20100*37180^4
657765^4+20100*58483^4=805515^4+20100*15983^4
522125^4+20100*66378^4=718045^4+20100*56072^4
408588^4+20100*68497^4=810588^4+20100*37231^4
318555^4+20100*78601^4=738645^4+20100*69899^4
329870^4+20100*80449^4=956990^4+20100*29407^4
405347^4+20100*82711^4=991597^4+20100*14477^4

Found 20 solutions.
Search finished successfully.

real 44m6.701s
user 43m56.375s
sys 0m10.106s

(以上)