#### 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