Geodesic
$\mathrm{Fibonacci}(n)$ modulo $n$ sequence
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2013), pp. 15-23

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the behavior of the $\mathrm{Fibonacci}(n)\mod n$ 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.
Keywords: Fibonacci sequence, remainders, Mathematica.
Mots-clés : congruence relation 
@article{VTGU_2013_4_a1,
     author = {V. M. Zyuz'kov},
     title = {$\mathrm{Fibonacci}(n)$ modulo $n$ sequence},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {15--23},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2013_4_a1/}
}
TY  - JOUR
AU  - V. M. Zyuz'kov
TI  - $\mathrm{Fibonacci}(n)$ modulo $n$ sequence
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2013
SP  - 15
EP  - 23
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTGU_2013_4_a1/
LA  - ru
ID  - VTGU_2013_4_a1
ER  - 
%0 Journal Article
%A V. M. Zyuz'kov
%T $\mathrm{Fibonacci}(n)$ modulo $n$ sequence
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2013
%P 15-23
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTGU_2013_4_a1/
%G ru
%F VTGU_2013_4_a1
V. M. Zyuz'kov. $\mathrm{Fibonacci}(n)$ modulo $n$ sequence. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2013), pp. 15-23. http://geodesic.mathdoc.fr/item/VTGU_2013_4_a1/