Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\)
type: Item
instance of: scholarly article
title: Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\)
zbMATH Open document ID: 1264.11022
author: Michael A. Bennett
author: Imin Chen
published in: Algebra \& Number Theory
publication date: 2012-08-10T00:00:00Z
full work available at URL: p04.xhtml
review text: The authors prove that, for any integer \(n\geq 3\), the Diophantine equation \(a^2+b^6=c^n\) has no nontrivial positive integer solutions with \(a\) and \(b\) coprime. The proof draws on the theory of Galois representations and modular forms, extending the techniques used to prove Fermat's last theorem and subsequent variants. The authors generalize to \(\mathbb{Q}\)-curves the multi-Frey technique developed by Siksek.
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11F80
zbMATH DE Number: 6064727
zbMATH Keywords: Fermat equations
zbMATH Keywords: Galois representations
zbMATH Keywords: \(\mathbb Q\)-curves
zbMATH Keywords: multi-Frey techniques
reviewed by: Nuria Vila
MaRDI profile type: Publication
OpenAlex ID: W33281010
DOI: 10.2140/ANT.2012.6.707
description: scientific article; zbMATH DE number 6064727