On the Diophantine equation \(x^2+q^{2k+1}=y^n\)
type: Item
instance of: scholarly article
title: On the Diophantine equation \(x^2+q^{2k+1}=y^n\)
zbMATH Open document ID: 1037.11021
author: Fadwa S. Abu Muriefah
author: S. Akhtar Arif
published in: Journal of Number Theory
publication date: 2002-09-12T00:00:00Z
review text: It is proved that if \(q\) is an odd prime, \(q \not \equiv 7 \pmod 8\), \(n\) is an odd integer \(> 5\), \(n\) is not a multiple of 3 and \((h,n) = 1\), where \(h\) is the class number of the field \( \mathbb{Q}(\sqrt{-q})\), then the Diophantine equation \(x^2 + q^{2k+1} = y^n\) has exactly two families of solutions \((q,n,k,x,y)\).
reviewed by: Edward L. Cohen
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 1800290
zbMATH Keywords: higher order Diophantine equations
zbMATH Keywords: Lucas sequence
zbMATH Keywords: primitive divisors
zbMATH Keywords: exponential Diophantine equation
MaRDI profile type: Publication
full work available at URL: jnth.2001.2750
OpenAlex ID: W2046199877
cites work: The diophantine equation \(x^2+3^m=y^n\)
cites work: Existence of primitive divisors of Lucas and Lehmer numbers (with an appendix by M. Mignotte)
cites work: The diophantine equation \(x^ 2 + 2^ k = y^ n\)
cites work: The diophantine equation x² + C = yⁿ
cites work: On an diophantine equation
cites work: Q5830719
DOI: 10.1006/JNTH.2001.2750
description: scientific article; zbMATH DE number 1800290