On the Diophantine equation \((x-1)^k+x^k+(x+1)^k=y^n\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1340.11045
DOI: 10.5486/PMD.2014.5815
author: Zhongfeng Zhang
published in: Publicationes Mathematicae Debrecen
publication date: 2014-08-14T00:00:00Z
Mathematics Subject Classification ID: 11D61
Mathematics Subject Classification ID: 11D59
zbMATH DE Number: 6330572
zbMATH Keywords: exponential Diophantine equations
zbMATH Keywords: modular forms
zbMATH Keywords: Thue equations
MaRDI profile type: Publication
full work available at URL: pmd.2014.5815
OpenAlex ID: W2318828912
title: On the Diophantine equation \((x-1)^k+x^k+(x+1)^k=y^n\)
review text: In the paper the title equation is solved for the values \(k=2,3,4\). In the proofs, the author uses results on generalized Ramanujan-Nagell equations, and applies the theory of modular forms for certain ternary equations.
reviewed by: Lajos Hajdu
description: scientific article; zbMATH DE number 6330572