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

Publication

Received: 22 August 2008
Accepted: 5 December 2008

Authors