On the greatest prime factor and divisibility properties of linear recursive sequences
type: Item
instance of: scholarly article
title: On the greatest prime factor and divisibility properties of linear recursive sequences
zbMATH Open document ID: 0704.11008
DOI: 10.1016/0019-3577(90)90035-L
published in: Indagationes Mathematicae. New Series
publication date: 1990-01-01T00:00:00Z
review text: Let K be an algebraic number field and \({\mathcal O}_ K\) its ring of integers. Let \(a_ 1,a_ 2\in K\) and \(\lambda\),mu\(\in {\mathcal O}_ K\), all non-zero. The author considers the numbers \(x_ m=a_ 1\lambda^ m+a_ 2\mu^ m\) \((m=0,1,2,...)\) and studies the problem for which n,m we have \(x_ n| x_ m\). In earlier papers by Parnami, Shorey and Steward this problem was considered in the case when the \(u_ m\) are rational integers. Presently, the author drops this constraint and manages to find effective lower bounds for m-2n and for the largest (in a suitable sense) prime factor in \(x_ m/(x_ m,x_ n)\).
Mathematics Subject Classification ID: 11D61
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 4154524
zbMATH Keywords: linear recurrence
zbMATH Keywords: algebraic number field
zbMATH Keywords: effective lower bounds
author: Attila Pethő
reviewed by: Frits Beukers
MaRDI profile type: Publication
cites work: Zur Transzendenz gewisser Reihen. (On the transcendence of certain series)
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full work available at URL: 0019-3577(90)90035-l
OpenAlex ID: W1975394101
description: scientific article; zbMATH DE number 4154524