On the Diophantine equation (xm−1)/(x−1) = (yn−1)/(y−1)

Bugeaud, Yann ; Shorey, T. N. (2002) On the Diophantine equation (xm−1)/(x−1) = (yn−1)/(y−1) Pacific Journal of Mathematics, 207 (1). pp. 61-75. ISSN 0030-8730

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Official URL: http://msp.berkeley.edu/pjm/2002/207-1/p04.xhtml

Abstract

We study the Diophantine equation xm−1 x−1 = yn−1 y−1 in integers x > 1, y > 1, m > 1, n > 1 with x≠y. We show that, for given x and y, this equation has at most two solutions. Further, we prove that it has finitely many solutions (x,y,m,n) with m > 2 and n > 2 such that gcd(m − 1,n − 1) > 1 and (m − 1) / (n − 1) is bounded.

Item Type:Article
Source:Copyright of this article belongs to Mathematical Sciences Publishers.
Keywords:Multiple Solution; Existence of Solution; Diophantine Equation; Number Theory
ID Code:67728
Deposited On:31 Oct 2011 13:27
Last Modified:31 Oct 2011 13:27

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