On the diophantine equation -: (x3-1)/(x-1)=(yn-1)/(y-1)

被引：18
|
作者：
Le, MH [1 ]
机构：
[1] Zhanjiang Teachers Coll, Dept Math, Zhanjiang, Guangdong, Peoples R China
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 351卷 / 03期
关键词：
D O I：
10.1090/S0002-9947-99-02013-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove that the equation (x(3) - 1)/(x - 1) = (y(n) - 1)/(y - 1), x,y,n is an element of N, x > 1, y > 1, n > 3, has only the solutions (x, y,n) = (5, 2, 5) and (90,2,13) with y is a prime power. The proof depends on some new results concerning the upper bounds for the number of solutions of the generalized Ramanujan-Nagell equations.
引用
收藏
页码：1063 / 1074
页数：12
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