A parametric family of quartic Thue inequalities
type: Item
instance of: scholarly article
title: A parametric family of quartic Thue inequalities
zbMATH Open document ID: 1254.11031
author: Bernadin Ibrahimpašic
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2011-05-23T00:00:00Z
full work available at URL: vol34 2 2.html
review text: Using an extended version of \textit{J. Worley}'s result [J. Aust. Math. Soc., Ser. A 31, 202--206 (1981; Zbl 0465.10026)] on rational approximations together with \textit{N. Tzanakis}' method [Acta Arith. 64, No. 3, 271--283 (1993; Zbl 0774.11014)] the author shows that the only primitive, integral solutions to the Diophantine inequality \[ |X^4- 2cX^3Y+2X^2Y^2+2cXY^3+Y^4|\leq 6c+4 \] with \(5\leq c \in \mathbb Z\), are \((\pm 1,0),(0,\pm 1),(1,\pm 1)\) and \((-1,\pm 1)\).
reviewed by: Volker Ziegler
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11D59
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 5899034
zbMATH Keywords: Thue equations
zbMATH Keywords: continued fractions
zbMATH Keywords: simultaneous Pellian equations
describes a project that uses: PARI/GP
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5899034