On the equation \(x^ n+(x+a)^ n=y^{2n}+(y+b)^{2n}\)
type: Item
instance of: scholarly article
title: On the equation \(x^ n+(x+a)^ n=y^{2n}+(y+b)^{2n}\)
zbMATH Open document ID: 0839.11015
DOI: 10.1016/0019-3577(95)93198-J
author: Marcin Mazur
author: Agata Smoktunowicz
published in: Indagationes Mathematicae. New Series
publication date: 1996-02-01T00:00:00Z
review text: Let \(n \geq 2\). It is proved that the equation in the title with \(a,b\) odd has only finitely many nontrivial solutions in integers \(x,y\). When \(a = b = 1\), the equation admits only the trivial solutions \(x = 0\), \(y \in \{0, -1\}\) or \(x = - 1\), \(y \in \{0, -1\}\) with \(n\) even.
Mathematics Subject Classification ID: 11D61
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 828209
zbMATH Keywords: higher degree diophantine equations
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 828209