关于整数的幂次之和表示的一个问题

On a problem of expressions of integers as powers

目的研究正整数的幂次之和表示的问题。方法利用椭圆曲线上的有理点的计算结果。结果得到4个有关正整数的幂次之和表示的命题。结论在平方和表示与立方和表示的情形下,存在无穷多个正整数具有两种不同的表示。

Aim To study the problem of expressions of positive integers as powers.Methods Using some results of the computation of rational points of elliptic curves.Results Some statements are obtained concerning the expressions of positive integers as powers.Conclusion In cases of squares and cubes expressions the conclusion is that there exist infinitely many integers which has two diferent such expressions.