On Cohn's conjecture concerning the Diophantine equation \(x^2+2^m=y^n\)
type: Item
instance of: scholarly article
title: On Cohn's conjecture concerning the Diophantine equation \(x^2+2^m=y^n\)
zbMATH Open document ID: 1006.11013
published in: Archiv der Mathematik
publication date: 2003-03-05T00:00:00Z
review text: In 1992, J.H.E. Cohn conjectured that the Diophantine equation \(x^2+2^m=y^n\) has no solution \((x,y,m,n)\) with \(m\) even, \(m\), \(n>2\) and \(y\) odd. The author proves this conjecture. This implies that this equation has only the solutions \((5,3,1,3)\), \((7,3,5,4)\) and \((11,5,2,3)\). The main tool is an estimate on linear forms in two logarithms of algebraic numbers, but the proof combines also results on several classical Diophantine equations.
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 1736501
zbMATH Keywords: exponential Diophantine equations
zbMATH Keywords: linear forms in two logarithms of algebraic numbers
Wikidata QID: Q123121989
author: Le Maohua
reviewed by: Maurice Mignotte
MaRDI profile type: Publication
full work available at URL: s00013-002-8213-5
OpenAlex ID: W2013612022
DOI: 10.1007/S00013-002-8213-5
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description: scientific article; zbMATH DE number 1736501