Vol. 2, No. 2, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 4, 547–726
Issue 3, 365–546
Issue 2, 183–364
Issue 1, 1–182

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
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
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