https://bbs1.rocketbbs.com/shochandas ja Tue, 13 Oct 2026 08:46:28 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3312 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。 Tue, 13 Oct 2026 08:46:28 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3301 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*112622336232835237^453194817657909603141924483163009761569312681243087128335374311482090011^4+18311*43729171208544681761515438580790369672494225775442469461224543103035425^4=330903342897730847670496434836982250471986013170858861765613657624221215^4+18311*41625975581597640641244765419207855225572150760989972783439450031700403^41351009... Sun, 11 Oct 2026 05:33:33 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3350 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 Thu, 08 Oct 2026 15:39:54 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3327 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*508274620746919056659507017910846170798143549458802386226050916102310017469150147097^411881441458873703278586240734651498013856866521... Wed, 07 Oct 2026 20:06:32 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3327 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*5089908598333393^41075444589480867400649396695836694447034562799521910485644157723210786^4+20078*82564180877232387257580375969290775570470777685811488087199510790987^4=1195843651757793929618824812013822399016372675484606104285735989572734^4+20078*57901391779181896540085759570691835074974077604000066994641799964619^412930624317913139987675... Wed, 07 Oct 2026 11:58:56 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3350 ２０２６^ｘ=８、１０１３^ｙ=４のとき、３/ｘ－２/ｙの値を求めよ。 Tue, 06 Oct 2026 20:50:50 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3329 -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*61^4308^4+20096*1243^4=14612^4+20096*587^41708^4+20096*1295^4=14620^4+20096*857^4124^4+20096*1363... Tue, 06 Oct 2026 11:26:23 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3327 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*160587561256127181729281787405237170584976871860772557197^4694021416105096410811890797144515236792589130770184482590320931506201450063552519242356481^4+20078*205408351012472883845049603752374267235099389266926570802855... Mon, 05 Oct 2026 21:04:14 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3329 -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*6^41127^4+20091*129^4=1489^4+20091*103^4942^4+20091*131^4=1608^4+20091*31^4893^4+20091*237^4=2003^... Mon, 05 Oct 2026 18:03:15 +0900 http://bbs1.rocketbbs.com/shochandas/posts/3329 -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*3361^471927^4+20086*7271^4=95401^4+20086*1367^474803^4+20086*8778^4=110619^4+20086*2536^... Mon, 05 Oct 2026 17:54:46 +0900