Stability classes of second-order linear recurrences modulo \(2^k\). II.
type: Item
instance of: scholarly article
title: Stability classes of second-order linear recurrences modulo \(2^k\). II.
zbMATH Open document ID: 1197.11023
DOI: 10.1216/RMJ-2010-40-1-85
author: Walter Carlip
author: Lawrence Somer
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-05-05T00:00:00Z
review text: The authors study second-order linear recurring sequences \(w_{i}= aw_{i-1}+ bw_{i-2}\) with integer parameters \(a,b\) and integer initial terms \(w_{0}\) and \(w_{1}.\) The modulo \(m\) reduced sequence is periodic with least period length \(\lambda (m)\). The authors consider the case \(m=p^{k}\) (prime power moduli) and study \(\lambda (p^{k})\) as well as the quantity \(\nu(d, p^{k})\) which denotes the number of times that the residue \(d\) appears in a single period. Let \[ \Omega (p^{k})= \{\nu(d,p^{k}): d \in\mathbb{Z}\} \] and define a sequence \((w_{i})\) to be stable modulo \(p\) if there is a positive integer \(N\) such that \(\Omega (p^{k})= \Omega (p^{N})\) for all \(k \geq N\). The main results of the present paper are concerned with stability properties modulo 2. In the case \(a\) odd and \(b \equiv 5\bmod 8\) a characterization is obtained. Part I, see Tatra Mt. Math. Publ. 20, 31--57 (2000; Zbl 0992.11013).
reviewed by: Robert F. Tichy
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11B50
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11K36
zbMATH DE Number: 5704107
zbMATH Keywords: Lucas
zbMATH Keywords: Fibonacci
zbMATH Keywords: distribution
zbMATH Keywords: stability
MaRDI profile type: Publication
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full work available at URL: rmj-2010-40-1-85
OpenAlex ID: W2006016800
description: scientific article; zbMATH DE number 5704107