椭圆曲线y^2=x^3+27x+62的整数点

The Integral Points on the Elliptic Curve y^2=x^3+27x+62

椭圆曲线的整数点是数论中的一个重要问题。关于椭圆曲线y^2=x^3+27x+62的整数点问题至今仍未解决。利用同余、Legendre符号的性质等初等方法证明了椭圆曲线y^2=x^3+27x+62无正整数点,从而推进了该类椭圆曲线的研究。

The integral points on elliptic curve are a very important problem of number theory.The integral points on the elliptic curve y-2=x-3＋27x＋62still remain unresolved.Using some properties of the solutions to congruence and Legendre symbol,it was proved that the elliptic curve y-2=x-3＋27x＋62has no positive integer points.These results promote the kind of elliptic curve.