On families of parametrized Thue equations
type: Item
instance of: scholarly article
title: On families of parametrized Thue equations
zbMATH Open document ID: 0934.11012
author: Clemens Heuberger
published in: Journal of Number Theory
publication date: 2000-04-02T00:00:00Z
review text: There is an extensive literature of parametric Thue equations [see \textit{C. Heuberger, A. Pethő} and \textit{R. F. Tichy} [Complete solution of parametrized Thue equations, Acta Math. Inform. Univ. Ostrav. 6, 93-113 (1998)]. The powerful result of the paper is a breakthrough in the sense that the author deals with a general type of parametric families of Thue equations, determined by several constants. Let \(d_2,\ldots,d_{n-1}\) \((n\geq 4)\) be pairwise distinct integers and \(a\) an integral parameter. Assuming \[ d_2+\ldots+d_{n-1}\neq 0\quad \text{or}\quad d_2\cdots d_{n-1}\neq 0 \] the author proves, that for \(a\geq a_0(n,d_2,\ldots,d_{n-1})\) all solutions of the equation \[ F_a(X,Y)=(X+aY)(X-d_2Y)(X-d_3Y)\cdots(X-d_{n-1}Y)(X-aY)-Y^n=\pm 1 \] are \((1,0),(-a,1),(d_2,1),(d_3,1),\ldots,(d_{n-1},1),(a,1)\) and their negatives. The ideas of the proof will certainly have further applications.
Mathematics Subject Classification ID: 11D59
zbMATH DE Number: 1310083
zbMATH Keywords: parametric families of Thue equations
reviewed by: István Gaál
MaRDI profile type: Publication
full work available at URL: jnth.1998.2348
OpenAlex ID: W2163392511
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DOI: 10.1006/JNTH.1998.2348
description: scientific article; zbMATH DE number 1310083