#### Vol. 2, No. 2, 2009

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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 $Q\left(n\right)$ which gives the ratio of the length of this period to $n$ itself. We compute $Q\left(n\right)$ 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 $n$
Primary: 11B39
Secondary: 11B50
##### Milestones
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