Difference between powers and squares of integers
type: Item
instance of: scholarly article
title: Difference between powers and squares of integers
zbMATH Open document ID: 0923.11055
author: Jean-Luc Lesage
published in: Journal of Number Theory
publication date: 1999-10-31T00:00:00Z
review text: Inspired by \textit{J. H. E. Cohn}'s conjecture [Acta Arith. 65, 367-381 (1993; Zbl 0795.11016)] the author establishes that for any solution in positive integers \(x,y,n\) of the diophantine equation \[ x^2+7=y^n, \] either \(x\in\{1, 3, 5, 11, 181\}\), or \(y>10^9\) and all prime factors of \(n\) exceed 5000. For fixed values of \(n\leq 5000\), the author uses the classical Thue equation approach (factorization and congruence considerations), and for fixed value of \(y\leq 10^9\) results from the theory of linear forms in logarithms are applied.
reviewed by: Roelof J. Stroeker
Mathematics Subject Classification ID: 11D61
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11J86
zbMATH DE Number: 1247928
zbMATH Keywords: exponential diophantine equations
zbMATH Keywords: higher degree equations
zbMATH Keywords: Thue equation approach
zbMATH Keywords: linear forms in logarithms
describes a project that uses: PARI/GP
MaRDI profile type: Publication
full work available at URL: jnth.1998.2303
OpenAlex ID: W1969629621
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DOI: 10.1006/JNTH.1998.2303
description: scientific article; zbMATH DE number 1247928