椭圆曲线y^2=nx(x^2+16)的整数点

Integral Points on Elliptic Curve y^2=nx(x^2+16)

如果n为无平方因子的正奇数,n的所有素奇数p_j(j∈Z^+)都满足P_j≡3,7(mod 8)为奇素数.主要利用同余、勒让德符号的性质等证明了椭圆曲线y^2=nx(x^2+16)当n≡3,7(mod 8)素数时除整点(0,0)以外,至多只有2组整数点.

Let “ n ” be a positive odd number,whose prime factors could be Pj≡ 3,7(mod 8),(j∈Z^+). It is proved that the elliptic curve y^2=nx(x^2+16) has only two positive integer points except (0,0) by some properties of congruence and the Legendre symbol.