ä»æ¥ãNHKEãã¬ãã®NHKé«æ ¡è¬åº§ æ°åŠïŒ©ãæçæ°ãïŒ10:30ïœ10:50ïŒãäœãšã¯ãªãã«èŠãŠããã
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A1,A2,A3,A4,A5,ãš
a1,a2,a3,a4,a5,ã®äžæè°ãªé¢ä¿ã§
A1=a1^2-a2^2
A2=2*a1*a2
ãšããã°
A1^2+A2^2=(a1^2-a2^2)^2+(2*a1*a2)^2
=a1^4-2*a1^2*a2^2+a2^4+4*a1^2*a2^2
=a1^4+2*a1^2*a2^2+a2^4
=(a1^2+a2^2)^2
A1=a1^2+a2^2-a3^2
A2=2*a1*a3
A3=2*a2*a3
ãšããã°
A1^2+A2^2+A3^2=(a1^2+a2^2-a3^2)^2+(2*a1*a3)^2+(2*a2*a3)^2
=(a1^2+a2^2)^2-2*(a1^2+a2^2)*a3^2+a3^4+4*(a1^2+a2^2)*a3^2
=(a1^2+a2^2)^2+2*(a1^2+a2^2)*a3^2+a3^4
=(a1^2+a2^2+a3^2)^2
åãã
A1=a1^2+a2^2+a3^2-a4^2
A2=2*a1*a4
A3=2*a2*a4
A4=2*a3*a4
ãšããã°
A1^2+A2^2+A3^2+A4^2=(a1^2+a2^2+a3^2-a4^2)^2+(2*a1*a4)^2+(2*a2*a4)^2+(2*a3*a4)^2
=(a1^2+a2^2+a3^2)^2-2*(a1^2+a2^2+a3^2)*a4^2+a4^4+4*(a1^2+a2^2+a3^2)*a4^2
=(a1^2+a2^2+a3^2)^2+2*(a1^2+a2^2+a3^2)*a4^2+a4^4
=(a1^2+a2^2+a3^2+a4^2)^2
以äžåæ§ã«ããŠ
äžè¬ã«
A1=a1^2+a2^2+a3^2+a4^2++(an-1)^2-an^2
A2=2*a1*an
A3=2*a2*an
A4=2*a3*an

An=2*(an-1)*an
ãšããŠããã°
A1^2+A2^2+A3^2++An^2=(a1^2+a2^2+a3^2++an^2)^2
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(1) m = 6, n = 3 ã®ãšã
(2) m = 7, n = 3 ã®ãšã
(3) m = 10, n = 4 ã®ãšã
(4) m = 11, n = 4 ã®ãšã
(5) m = 12, n = 4 ã®ãšã
ââã以äžããã¿ãã¬æ³šæãââ
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(2),(5) ã¯äžå¯èœã
(4) ã¯æªè§£æ±ºã§ãã
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(6) m ⊠3^t + 1 , n = 2 * t ã®ãšããåœç©2æãç¹å®å¯èœ
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(63,16),(33,56),(-33,56),(-63,16),(-63,-16),(-33,-56),(33,-56),(63,-16)
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8ãçãã2蟺ã«å¯Ÿãæ®ãäžèŸºã®é·ãã4,11,14ã®äºç蟺äžè§åœ¢ããããã1,1,2åã§åãããš8ã®åã«å
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12=> 6;12;21 :2;3;1 (å
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13=> 1;22;23 :1;2;1 (å
æ¥åè§åœ¢)
13=> 10;13;24 :1;3;1 (å
æ¥äºè§åœ¢)
13=> 1;13;22 :2;2;2
14=> 4;22;26 :1;2;1
14=> 14;22;26 :2;1;1
16=> 8;22;28 :1;1;2
16=> 4;24;31 :1;2;1
16=> 17;22;28 :1;2;1
16=> 7;16;20 :1;3;2
16=> 4;16;31 :2;3;1
16=> 8;16;28 :2;3;1
16=> 12;16;23 :2;3;1
16=> 4;16;18 :3;3;2
16=> 4;18;31 :5;2;1
17=> 16;17;30 :1;3;1
18=> 4;18;24 :1;3;2
18=> 6;18;34 :2;3;1
18=> 12;18;28 :2;3;1
19=> 11;26;37 :1;2;1
19=> 11;19;26 :1;4;1
19=> 19;26;37 :2;1;1
19=> 11;19;26 :2;2;2
20=> 10;20;35 :2;3;1

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13=> 1;13;22 :1;4;1
13=> 13;22;23 :2;1;1
14=> 4;14;22 :2;2;2
15=> 15;18;24 :3;1;1
15=> 3;14;25 :2;2;2
15=> 14;19;25 :1;1;2
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# 11ã¯3ã¿ã€ãã«ã¯åããããªãããã§ãã
ãã2æ¡ã®æ°Nã
1ãã9ãŸã§ã®æ°åã䜿ã
N=a^2+b^2=c^2+d^2+e^2=f^2-d^2+g^2=h^2+i^2
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(a,b,c,d,e,f,g,h,i)=(1,8,2,5,6,3,9,4,7)
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H(t)=10^3*(sqrt((6400*cos(Ξ)*tan(t/240))^2+(6400*cos(Ξ))^2)-6400*cos(Ξ)) (m)
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H(t)=10^3*(sqrt((6400*cos(36*Pi/180)*tan(t/240*Pi/180))^2+(6400*cos(36*Pi/180))^2)
-6400*cos(36*Pi/180))ã(m)
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t ;H(t)(m)
10;1.369115132
20;5.476464147
30;12.32205791
40;21.90591451
50;34.22805931
60;49.28852487
70;67.08735103
80;87.62458486
90;110.9002806
100;136.9145000
110;165.6673116
120;197.1587915
130;231.3890231
140;268.3580969
150;308.0661105
160;350.5131691
170;395.6993849
180;443.6248773
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(1^2+4^2+7^2+8^2+9^2+10^2+14^2+15^2+18^2=33*32(=1056))
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Positions of ones in binary expansion of Euler's constant gamma.
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Euler's constant gamma
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γ:=lim(n->â)(â[k=1,n]1/k-log(n))=0.57721
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