On Le's and Bugeaud's papers about the equation \(ax^2 + b^{2m-1} = 4c^p\)
type: Item
instance of: scholarly article
title: On Le's and Bugeaud's papers about the equation \(ax^2 + b^{2m-1} = 4c^p\)
zbMATH Open document ID: 1012.11023
published in: Monatshefte für Mathematik
publication date: 2002-12-01T00:00:00Z
review text: This paper corrects an inacurracy which appeared in papers of M. H. Le, M. Mignotte and D. Bugeaud on the generalized Ramanujan-Nagell equation. In a paper published in Monatsh. Math. 120, 121--125 (1995; Zbl 0877.11020), \textit{M. H. Le} claimed that the equation \(ax^2+b^{2m-1}=4c^p\) has only finitely many solutions in positive integers with \(\gcd(ax,b)=1\) when \(p>5\) is a prime which does not divide the class number of \({\mathbb Q}(\sqrt{-ab})\). The author gives a counter-example with \(p=7\), and he proves that the results of the previous papers can be obtained under the extra assumption that \(b\) is a square-free integer.
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 1837284
zbMATH Keywords: Ramanujan-Nagell equation
zbMATH Keywords: Lucas numbers
zbMATH Keywords: exponential Diophantine equations
author: Yuri Bilu
reviewed by: Maurice Mignotte
MaRDI profile type: Publication
full work available at URL: s00605-001-0471-y
OpenAlex ID: W183055916
DOI: 10.1007/S00605-001-0471-Y
description: scientific article; zbMATH DE number 1837284