Pentagonal numbers in the associated Pell sequence and Diophantine equations \(x^2(3x-1)^2=8y^2\pm 4\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1012.11015
author: V. Siva Rama Prasad
author: B. Srinivasa Rao
publication date: 2002-07-03T00:00:00Z
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11D25
zbMATH DE Number: 1656217
zbMATH Keywords: quartic Diophantine equation
zbMATH Keywords: generalized pentagonal numbers
zbMATH Keywords: Pell sequence
zbMATH Keywords: integral solutions
MaRDI profile type: Publication
title: Pentagonal numbers in the associated Pell sequence and Diophantine equations \(x^2(3x-1)^2=8y^2\pm 4\)
published in: The Fibonacci Quarterly
review text: Here the authors prove that the only generalized pentagonal numbers (integers of the form \(m(3m-1)/2\)) in the associated Pell sequence \(Q_{n+2}=2Q_{n+1}+Q_n\), where \(Q_0=Q_1=1\), are 1 and 7. Since \(x=Q_n\) gives all integral solutions of the Diophantine equations \(x^2-2y^2=\pm 1\), all integral solutions of \(x^2(3x-1)^2=8y^2\pm 4\) are obtained as a corollary.
reviewed by: Ming Luo
description: scientific article; zbMATH DE number 1656217