Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 731482, 3 pages
http://dx.doi.org/10.1155/2013/731482
Research Article

On Period of the Sequence of Fibonacci Polynomials Modulo

İnci Gültekin1 and Yasemin Taşyurdu2

1Department of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey
2Department of Mathematics, Faculty of Science and Letters, Erzincan University, 24000 Erzincan, Turkey

Received 20 November 2012; Revised 21 January 2013; Accepted 23 January 2013

Academic Editor: Binggen Zhang

Copyright © 2013 İnci Gültekin and Yasemin Taşyurdu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is shown that the sequence obtained by reducing modulo coefficient and exponent of each Fibonacci polynomials term is periodic. Also if is prime, then sequences of Fibonacci polynomial are compared with Wall numbers of Fibonacci sequences according to modulo . It is found that order of cyclic group generated with matrix is equal to the period of these sequences.