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楼主 |
发表于 2019-3-8 17:09
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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 = 5; 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-----{{10,55},{25,50},{38,41}}
2-----13-----{{117,598},{122,597},{338,507}}
3-----17-----{{289,1156},{404,1121},{799,884}}
4-----29-----{{1475,4282},{1682,4205},{1885,4118}}
5-----37-----{{1369,8214},{3959,7326},{5646,6121}}
6-----41-----{{2476,10475},{4715,9676},{6724,8405}}
7-----53-----{{3647,20122},{5618,19663},{13727,15158}}
8-----61-----{{9475,27474},{14274,25315},{18605,22326}}
9-----73-----{{10072,44403},{15987,42632},{21608,40077}}
10-----89-----{{7832,74315},{25525,70232},{39605,63368}}
11-----97-----{{28809,88076},{37636,84681},{46071,80404}} |
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