On squares in certain Lucas sequences
type: Item
instance of: scholarly article
title: On squares in certain Lucas sequences
zbMATH Open document ID: 0795.11007
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1994-05-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93586
review text: Let \(a\) be an integer \(\geq 3\). The Lucas sequence \(u_ n= (\alpha^ n- \beta^ n)/ (\alpha-\beta)\), for \(\alpha= (a+ \sqrt{a^ 2-4})/2\) and \(\beta= (a- \sqrt{a^ 2-4})/2\), is considered. It is proved that for \(a\geq 4\), \(u_ n\) is neither a square, nor a double or a triple square, nor six times a square for \(n>3\), except for \(a=338\) and \(n=4\).
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 556382
zbMATH Keywords: square values
zbMATH Keywords: Lucas sequence
author: Maurice Mignotte
author: Attila Pethő
reviewed by: Edward L. Cohen
MaRDI profile type: Publication
OpenAlex ID: W2012851991
cites work: Q4696640
cites work: Q4692759
cites work: THE EQUATIONS 3x2−2 = y2 AND 8x2−7 = z2
cites work: Minorations de Combinaisons Linéaires de Logarithmes de Nombres Algébriques
cites work: Linear forms in two logarithms and Schneider's method (III)
cites work: The diophantine equation \(x^ 4 - kx^ 2 y^ 2 + y^ 4 = 1\)
DOI: 10.5802/JTNB.97
description: scientific article; zbMATH DE number 556382