椭圆曲线y^(2)=x^(3)+33x±74的整数点

The Integral Points on the Elliptic Curve y^(2)=x^(3)+33x±74

本文利用同余、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讨论了椭圆曲线y^(2)2=x^(3)±33x±74的整数点,最终得到了这两个椭圆曲线没有正整数点的结论,即它们仅有过y=0的整数点.

In this paper,the integer points on the elliptic curve y^(2)=x^(3)+33x±74are discussed by means of congruence,odd-even analysis,quadratic congruence and the recursive properties of solutions of binary quadratic equations.Then,the conclusion that two elliptic curves y^(2)=x^(3)+33x±74 have no positive integer points is reached.