Square-classes in Lucas sequences having odd parameters
type: Item
instance of: scholarly article
title: Square-classes in Lucas sequences having odd parameters
zbMATH Open document ID: 0923.11037
author: Wayne L. McDaniel
author: Paulo Ribenboim
published in: Journal of Number Theory
publication date: 1999-06-20T00:00:00Z
review text: Two or more terms of a sequence are said to be in the same square-class if the squarefree parts of the terms are identical. Let \(\{U_n (P,Q)\}\) and \(\{V_n(P,Q)\}\) denote the Lucas sequence and companion Lucas sequence, respectively, with parameters \(P\) and \(Q\). For all relatively prime values of \(P\) and \(Q\) with discriminant \(P^2-4Q>0\), it is shown that \(\{U_n(P,Q) \}\) and \(\{V_n(P,Q)\}\) have only finitely many nontrivial square-classes and each square-class contains at most three terms. The square-classes are explicitly determined in ``most'' cases, and an effectively computable bound on the number of square-classes, depending on \(P\) and \(Q\), is obtained in the remaining cases.
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11D09
zbMATH DE Number: 1268041
zbMATH Keywords: quadratic diophantine equations
zbMATH Keywords: Lucas sequence
zbMATH Keywords: square-classes
Wikidata QID: Q114234195
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
full work available at URL: jnth.1998.2280
OpenAlex ID: W2060212722
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DOI: 10.1006/JNTH.1998.2280
description: scientific article; zbMATH DE number 1268041