On the Diophantine equation (xk-1)(yk-1) = (zk-1)

被引：7

作者：

Bugeaud, Y ^{[1
]}

机构：

[1] Univ Strasbourg, UFR Math, 7 Rue Rene Descartes, F-67084 Strasbourg, France

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2004年 / 15卷 / 01期

关键词：

D O I：

10.1016/S0019-3577(04)90002-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k greater than or equal to 3 be an integer. We study the possible existence of pairs of distinct positive integers (a, b) such that any of the three numbers a + 1, b + 1, and ab + 1 is a k-th power. We further investigate several related questions.

引用

页码：21 / 28

页数：8

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