On the distribution of the residues of the Fibonacci sequence \(\text{mod } 5c\) (Q1902314)
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scientific article; zbMATH DE number 818413
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the distribution of the residues of the Fibonacci sequence \(\text{mod } 5c\) |
scientific article; zbMATH DE number 818413 |
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On the distribution of the residues of the Fibonacci sequence \(\text{mod } 5c\) (English)
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11 February 1996
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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 \(c\).
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Fibonacci numbers
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length of the period
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