Solving a family of quartic Thue inequalities using continued fractions
type: Item
instance of: scholarly article
title: Solving a family of quartic Thue inequalities using continued fractions
zbMATH Open document ID: 1244.11029
DOI: 10.1216/RMJ-2011-41-4-1173
author: Andrej Dujella
author: Borka Jadrijević
author: Bernadin Ibrahimpašic
published in: Rocky Mountain Journal of Mathematics
publication date: 2011-08-19T00:00:00Z
review text: In the paper under review the authors consider the Thue inequality \[ |x^4+2(1-n^2)x^2y^2+y^4|\leq 2n+3 \] and prove that for \(n\geq 3\) the only primitive solutions are \((0,\pm 1)\) and \((\pm 1,0)\), if \(2(n^2-1)\) is not a perfect square. It has the additional primitive solutions \((\pm 1,\pm \nu)\) and \((\pm \nu,\pm 1)\) only if \(2(n^2-1)=\nu^2\). The authors obtain their result by applying \textit{N. Tzanakis} method [Acta Arith. 64, No.3, 271--283 (1993; Zbl 0774.11014)] and using a generalization of \textit{R. T. Worley}'s theorem on Diophantine approximations [J. Aust. Math. Soc., Ser. A 31, 202--206 (1981; Zbl 0465.10026)].
reviewed by: Volker Ziegler
Mathematics Subject Classification ID: 11D59
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 5940453
zbMATH Keywords: Thue equations
zbMATH Keywords: simultaneous Pellian equations
zbMATH Keywords: continued fractions
Wikidata QID: Q57595878
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5940453