Bounds for Fibonacci period growth

Chuya Guo; Alan Koch

doi:10.2140/involve.2009.2.195

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Home > Journals > Involve > Volume 2 > Issue 2 > Article

2009 Bounds for Fibonacci period growth

Chuya Guo, Alan Koch

Involve 2(2): 195-210 (2009). DOI: 10.2140/involve.2009.2.195

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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 $n$ .