On Period of Generalized Fibonacci Sequence Over Finite Ring and Tridiagonal Matrix

Yıl 2017, Cilt: 13 Sayı: 1, 165 - 169, 30.03.2017

Yasemin Taşyurdu Zülküf Dilmen

https://doi.org/10.18466/cbayarfbe.302663

Öz

In this study,



















 Fibonacci sequence was defined over an
arbitrary ring and its some properties are investigated. The terms of this sequence are derivated by Tridiagonal determinant of the matrix.
It was shown that this sequence is periodic and their period is obtained. It
was shown that the sequence obtained by reducing modulo

 coefficient and exponent of each Fibonacci
sequence in arbitrary rings is periodic. It was seen that order of cyclic group
generated with matrix

  is
equal to the period of this sequence where

 are
arbitrary elements of the ring.  Also, the
period of this sequence is compared with Wall number of Fibonacci sequence and it
was shown that this period always was an even number.

Anahtar Kelimeler

Fibonacci Sequence, Finite Ring, Period

Kaynakça

• Taşyurdu, Y.; Gültekin, İ., The Period of Fibonacci Sequences Over The Finite Field of Order p^2, New Trends in Mathematical Sciences. 2016; 4, 248-255.