椭圆曲线y^2=nx(x^2+64)的整数点

Integral Points on Elliptic Curve y^2=nx(x^2+64)

如果n为无平方因子的正奇数,n的所有素因素p_i(i∈Z+)都满足p_i≡3,7(mod8),则椭圆曲线y^2=nx(x^2+64)除整数点(x,y)=(0,0)外至多有一个整数点.

Let n be an positive odd number,which prime factors could be pi≡3,7（mod8）,i∈Z^＋.Then in addition to（x,y）=（0,0）,the elliptic curve y^2=nx（x^2＋64）has one integer point at most.