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楼主 |
发表于 2019-3-8 08:33
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费马小定理3
若 4x+1= p 为素数,
则 p^1 = a^2+b^2 (一组解)
则 p^2 = a^2+b^2 (一组解)
则 p^3 = a^2+b^2 = c^2+d^2(两组解)
则 p^4 = a^2+b^2 = c^2+d^2(两组解)
则 p^5 = a^2+b^2 = c^2+d^2 = e^2+f^2(三组解)
则 p^6 = a^2+b^2 = c^2+d^2 = e^2+f^2(三组解)
s = 0;
For[n = 4; x = 1, x <= 24, x++, If[PrimeQ[4 x + 1], s = s + 1;
Print[s, "-----", 4 x + 1, "-----",
PowersRepresentations[(4 x + 1)^n, 2, 2]]]]
1-----5-----{{0,25},{7,24},{15,20}}
2-----13-----{{0,169},{65,156},{119,120}}
3-----17-----{{0,289},{136,255},{161,240}}
4-----29-----{{0,841},{41,840},{580,609}}
5-----37-----{{0,1369},{444,1295},{840,1081}}
6-----41-----{{0,1681},{369,1640},{720,1519}}
7-----53-----{{0,2809},{1241,2520},{1484,2385}}
8-----61-----{{0,3721},{671,3660},{1320,3479}}
9-----73-----{{0,5329},{721,5280},{3504,4015}}
10-----89-----{{0,7921},{3471,7120},{4879,6240}}
11-----97-----{{0,9409},{959,9360},{6305,6984}} |
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