Bounds for Fibonacci period growth

Guo, Chuya; Koch, Alan

doi:10.2140/involve.2009.2.195

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-4184 (e-only)

ISSN: 1944-4176 (print)

Author Index

Coming Soon

Other MSP Journals

Bounds for Fibonacci period growth

Chuya Guo and Alan Koch

Vol. 2 (2009), No. 2, 195–210

DOI: 10.2140/involve.2009.2.195

Abstract

We study the Fibonacci sequence mod $n$ for some positive integer $n$ . Such a sequence is necessarily periodic; we introduce a function $Q (n)$ which gives the ratio of the length of this period to $n$ itself. We compute $Q (n)$ in certain cases and provide bounds for it which depend on the nature of the prime divisors of $n$ .

Keywords

Fibonacci sequence, Fibonacci periods, growth of Fibonacci periods, Fibonacci period mod $n$

Mathematical Subject Classification 2000

Primary: 11B39

Secondary: 11B50

Milestones

Received: 22 August 2008

Accepted: 5 December 2008

Published: 7 May 2009

Communicated by Arthur T. Benjamin

Authors

Chuya Guo
Agnes Scott College Department of Mathematics 141 E. College Ave. Decatur, GA 30030 United States

Alan Koch
Agnes Scott College Department of Mathematics 141 E. College Ave. Decatur, GA 30030 United States

Vol. 2, No. 2, 2009