Finiteness results for \(F\)-Diophantine sets
type: Item
instance of: scholarly article
title: Finiteness results for \(F\)-Diophantine sets
zbMATH Open document ID: 1396.11056
author: Attila Bérczes
author: Andrej Dujella
author: Lajos Hajdu
author: Szabolcs Tengely
published in: Monatshefte für Mathematik
publication date: 2016-08-01T00:00:00Z
review text: Let \(F\in \mathbb Z[X,Y]\) be a bivariate polynomial, then the authors of the paper under review call a set \(A\subseteq \mathbb Z\) \((F,m)\)-Diophantine if \(F(a,b)\) is an \(m\)-th power for any \(a,b\in A\) with \(a\neq b\). In case that \(F(x,y)=xy+1\) and \(m=2\) this definition coincides with classical Diophantine tuples. Under some mild technical assumptions they show finiteness results for \((F,m)\)-Diophantine sets. In particular, they give a complete characterization of all pairs \((F,m)\) for which infinite \((F,m)\)-Diophantine sets exist.
reviewed by: Volker Ziegler
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 6608234
zbMATH Keywords: Diophantine sets
zbMATH Keywords: polynomials in two variables
zbMATH Keywords: binary forms
zbMATH Keywords: power values of polynomials
describes a project that uses: SageMath
MaRDI profile type: Publication
full work available at URL: s00605-015-0824-6
OpenAlex ID: W2117630672
Wikidata QID: Q57595806
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DOI: 10.1007/S00605-015-0824-6
description: scientific article; zbMATH DE number 6608234