摘要
In this paper, we have proved the following theorems with method of more elementary and more clear. Theorem 1 The Diophantine equation (x^m-1)/(x-1)=y^2, m>2, |x|>1 has no solution in integers m, x, y, except m=4, x=7, y=±20 and m=5, x=3, y=±11. Theorem 2 For any given integers x, y, let N(x, y) be the number of solutions of the equation (x^m-1)/x-1=y^n,m>2,n>1, then we have N(x, y)≤1.
基金
中国科学院青年奖励研究基金
