同余数判别的两个新定理
首发时间:2019-06-10
摘要:本文发现了两个新的非同余数的判别定理:1)设p,q为素数,且p,q≡3(mod 8),则2pq不是同余数;设p,q为为素数,且p,q≡5(mod 8),则2pq不是同余数。这两个定理不依赖于BSD猜想,结论简单明了,计算复杂性为O(√n)。
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Two New theorem for congruence detection
Abstract: Two new discriminant theorems for non-congruent Numbers are found in this paper. 1) If p and q are prime, and p,q≡3(mod 8), then 2pq is not congruent numbers; 2).If p and q are prime, and p,q≡5(mod 8), then 2pq is not congruent numbers. These two theorems do not rely on the BSD conjecture, the conclusion is simple and straightforward, the computational complexity is O (√n)..
Keywords: congruence number;Elliptic Curves;Number Number Theory Algebraic geometry
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