On the family of Diophantine triples \(\{k+1,4k,9k+3\}\)
type: Item
instance of: scholarly article
title: On the family of Diophantine triples \(\{k+1,4k,9k+3\}\)
zbMATH Open document ID: 1199.11075
author: Bo He
author: Alain Togbé
published in: Periodica Mathematica Hungarica
publication date: 2009-12-29T00:00:00Z
review text: The paper provides an extendibility result concerning a parametric family of Diophantine triples. The authors prove that if \(k\) and \(d\) are positive integers such that the product of any two distinct elements of the set \(\{k+1,4k,9k+3,d\}\) increased by \(1\) is a perfect square, then \(d=144k^3+192k^2+76k+8\).
reviewed by: Lajos Hajdu
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11D45
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11J68
Mathematics Subject Classification ID: 11J86
zbMATH DE Number: 5651911
zbMATH Keywords: Diophantine \(m\)-tuple
zbMATH Keywords: Pell equation
zbMATH Keywords: Diophantine approximation
zbMATH Keywords: linear forms in logarithms
MaRDI profile type: Publication
full work available at URL: s10998-009-9059-6
OpenAlex ID: W2023146651
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DOI: 10.1007/S10998-009-9059-6
description: scientific article; zbMATH DE number 5651911