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Bounds for Fibonacci period growth. (English) Zbl 1225.11020
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 $$m$$)
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