Divisibility properties of binary recurrent sequences
type: Item
instance of: scholarly article
title: Divisibility properties of binary recurrent sequences
zbMATH Open document ID: 1001.11010
DOI: 10.1016/S0019-3577(01)80016-1
author: Florian Luca
published in: Indagationes Mathematicae. New Series
publication date: 2002-07-11T00:00:00Z
review text: Let \(P\) be any set of primes and \((u_n)_{n\geq 0}\) be a nondegenerate binary recurrence whose \(n\)th term is given by \(u_n= c\alpha^n+ d\beta^n\). The author proves: If \(c/d\) and \(\alpha/\beta\) are multiplicatively independent, then there exist two effectively computable constants \(c_1\) and \(c_2\) depending on the sequence \((u_n)_{n\geq 0}\) and the set \(P\) such that whenever \(m\neq n\) are two integers with \(u_m/u_n\) an \(S\)-integer and \(n> c_1\), then \(m> c_2 \frac{n^2}{\log n}\). There is another statement about the multiplicatively dependent case.
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 1766476
zbMATH Keywords: divisibility
zbMATH Keywords: binary recurrence
reviewed by: Kálmán Liptai
MaRDI profile type: Publication
cites work: Logarithmic forms and group varieties.
cites work: A Full Characterisation of Divisibility Sequences
cites work: Effective lower bound for the \(p\)-adic distance between powers of algebraic numbers
cites work: Zur Transzendenz gewisser Reihen. (On the transcendence of certain series)
cites work: Linear forms in two logarithms and interpolation determinants
cites work: On the greatest prime factor and divisibility properties of linear recursive sequences
cites work: Primitive divisors of the expression An - Bn in algebraic number fields.
cites work: Q4146788
cites work: Q3744223
cites work: Q4296321
description: scientific article; zbMATH DE number 1766476