关于椭圆曲线y^(2)=(x+47)(x^(2)+47^(2))的整数点

Integral Points on Elliptic Curve y^(2)=(x+47)(x^(2)+47^(2))

设P为奇素数,研究了椭圆曲线y^(2)=(x+P)(x^(2)+P^(2))的整数点问题。运用初等方法证明了该椭圆曲线在P=47时,仅有整数点(x,y)=(-47,0)。

Let P be odd prime.This article studies the problem of the integral points on the elliptic curves y^(2)=(x+47)(x^(2)+47^(2)).The elementary method is used to prove the elliptic curve has only integral point(x,y)=(-47,0)when P=47.