Bounds for Fibonacci period growth. (English) Zbl 1225.11020

Guo, Chuya; Koch, Alan

Involve 2, No. 2, 195-210 (2009).

Summary: 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 \(n\).

MSC:

11B39	Fibonacci and Lucas numbers and polynomials and generalizations
11B50	Sequences (mod \(m\))

Keywords:

Fibonacci sequence; Fibonacci periods; growth of Fibonacci periods; Fibonacci period mod n