Vol. 2, No. 2, 2009

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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