Extension of a parametric family of Diophantine triples in Gaussian integers
type: Item
instance of: scholarly article
title: Extension of a parametric family of Diophantine triples in Gaussian integers
zbMATH Open document ID: 1374.11042
author: A. Bayad
author: Alan Filipin
author: Alain Togbé
published in: Acta Mathematica Hungarica
publication date: 2017-03-31T00:00:00Z
review text: A Diophantine \(m\)-tuple in a ring \(R\) is a set of the form \(\{a_1,\dots,a_m\}\subset R\) with \(a_ia_j+1\) being a square in \(R\) for all \(i\neq j\). The authors prove that if \(\{k, 4k + 4, 9k + 6, d\}\), where \(k\in\mathbb{Z}[i]\), \(k\neq 0,-1\), is a Diophantine quadruple in the ring \({\mathbb Z}[i]\), then \(d = 144k^3 + 240k^2 + 124k + 20\).
reviewed by: Lajos Hajdu
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11J68
zbMATH DE Number: 6699240
zbMATH Keywords: Diophantine tuple
zbMATH Keywords: simultaneous Diophantine equations
MaRDI profile type: Publication
full work available at URL: s10474-016-0581-6
OpenAlex ID: W2288779371
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DOI: 10.1007/S10474-016-0581-6
description: scientific article; zbMATH DE number 6699240