A small contribution to Catalan's equation
type: Item
instance of: scholarly article
title: A small contribution to Catalan's equation
zbMATH Open document ID: 0796.11013
author: A. M. W. Glass
author: David B. Meronk
author: Taihei Okada
author: Ray Phillip Steiner
published in: Journal of Number Theory
publication date: 1994-06-08T00:00:00Z
review text: Let \(x\), \(y\), \(m\), \(n\) be a non-trivial solution of the so-called Catalan's equation \(x^ m- y^ n=1\). It is shown that the greatest prime factors of the exponents are bounded by \(3.42\cdot 10^{28}\) and \(5.6\cdot 10^{19}\), respectively. The proof is essentially based on Tijdeman's argument and some recent developments in the effective theory of linear forms in logarithms done by Mignotte and Waldschmidt.
Mathematics Subject Classification ID: 11D61
Mathematics Subject Classification ID: 11J86
zbMATH DE Number: 584036
zbMATH Keywords: Catalan equation
zbMATH Keywords: greatest prime factors of the exponents
zbMATH Keywords: linear forms in logarithms
reviewed by: Bela Brindza
MaRDI profile type: Publication
full work available at URL: jnth.1994.1030
OpenAlex ID: W1985271743
DOI: 10.1006/JNTH.1994.1030
description: scientific article; zbMATH DE number 584036