Fibonacci(n) modulo sequence | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2013. № 4(24).

Fibonacci(n) modulo sequence

We study the behavior of the Fibonacci (n) mod n sequence and pay attention to some subsequences: n runs through the set of prime numbers and the cases with n = qp, where p runs through the set of prime numbers and q is a fixed natural number. The behavior of the sequence is investigated using the Mathematica system. Some hypotheses are formulated and proved.

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Keywords

последовательность чисел Фибоначчи, остатки от деления, сравнения, система Mathematica, Fibonacci sequence, remainders, congruence relation, Mathematica

Authors

Name	Organization	E-mail
Zyuz'kov Valentin Mikhailovich	Tomsk State University	vmz@math.tsu.ru

Всего: 1

References

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Kramer J. and V.E. Hoggatt, Jr. Special cases of Fibonacci periodicity // The Fibonacci Quarterly. 1972. 10:5 (Nov.). P. 519-522.

Воробьев Н.Н. Числа Фибоначчи. М.: Наука, 1978. 144 с.

Desmond J.E. Problem B-182 // The Fibonacci Quarterly. 1970. 20:1 (Feb.). P. 96.