椭圆曲线y^(2)=x^(3)-x±6的整数点

The integral points on the elliptic curve y^(2)=x^(3)-x±6

利用同余、奇偶分析、二次同余式及二元二次方程解的结构及解序列的递归性质等初等方法,研究了椭圆曲线y^(2)=x^(3)-x±6的整点问题,得到了椭圆曲线y^(2)=x^(3)-x±6没有正整数点的结论.

By using congruence,parity analysis,quadratic congruence,the structure of solutions of quadratic equations with two variables and the recursive properties of solution sequence,the integral point problem of elliptic curve y^(2)=x^(3)-x±6 is studied,and the conclusion is obtained that elliptic curve has no positive integer points.