On the Diophantine equation \(x^ 2+a^ 2=2y^ p\).
type: Item
instance of: scholarly article
title: On the Diophantine equation \(x^ 2+a^ 2=2y^ p\).
zbMATH Open document ID: 1088.11021
DOI: 10.1016/S0019-3577(04)90021-3
published in: Indagationes Mathematicae. New Series
publication date: 2005-01-03T00:00:00Z
review text: The author combines lower bounds for two logarithms (in the complex case) with elementary arguments to provide an effective method to solve completely instances of the exponential Diophantine equations \(x^2+a^2=2y^p\) and \(x^2+a^2=y^p\). As examples, he solves completely the first equation for \(a\) odd, \(3\leq a \leq 305\), and the second one for \(a\) odd, \(3\leq a \leq 501\).
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11D25
zbMATH DE Number: 2124645
zbMATH Keywords: exponential Diophantine equations
zbMATH Keywords: Diophantine approximations
author: Szabolcs Tengely
reviewed by: Maurice Mignotte
MaRDI profile type: Publication
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full work available at URL: s0019-3577(04)90021-3
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description: scientific article; zbMATH DE number 2124645