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On the distribution of the residues of the Fibonacci sequence \(\text{mod } 5c\). (Zur Verteilung der Reste der Fibonacci-Folge modulo \(5c\).) (German) Zbl 0837.11010

It is well known that for each integer \(m\) larger than one, the sequence of Fibonacci numbers modulo \(m\) is purely periodic. In this paper the length of the period of these sequences for \(m\) a multiple of 5 is studied. Let \(h(m)\) be the length of the period of the Fibonacci sequence modulo \(m\). Then for example the following is shown: For all integers \(c > 1\) the number \(h(5c)/h(c)\) is an integer and it is a divisor of 20. Further the form of the period modulo \(5c\) is compared with the form of the period modulo \(c\).

MSC:

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