The Diophantine equation \((a^n-1)(b^n-1)=x^2\)
type: Item
instance of: scholarly article
title: The Diophantine equation \((a^n-1)(b^n-1)=x^2\)
zbMATH Open document ID: 1012.11024
DOI: 10.1023/A:1019688312555
author: J. H. E. Cohn
published in: Periodica Mathematica Hungarica
publication date: 2003-05-18T00:00:00Z
review text: In earlier papers, \textit{L. Szalay} [Publ. Math. 57, 1-9 (2000; Zbl 0961.11013)] and \textit{L. Szalay} and \textit{L. Hajdu} [Period. Math. Hung. 40, 141-145 (2000; Zbl 0973.11015)] completely solved the title equation when \(\{a,b\}=\{2,3\},\{2,2^k\}\), and \(\{a,b\}=\{2,6\},\{a,a^k\}\), respectively. In the present paper the author considerably generalizes these theorems. Among other results, in the case \(a^l=b^k\) all solutions of the title equation are described. The author completely solves the title equation when \(2\leq a<b\leq 12\) and \(\{a,b\}\neq\{2,10\}\), as well. Some interesting conjectures are also formulated.
reviewed by: Lajos Hajdu
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 1912047
zbMATH Keywords: exponential Diophantine equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1912047