Advances in Difference Equations
Volume 2008 (2008), Article ID 143943, 9 pages
doi:10.1155/2008/143943
Research Article
On the Solutions of Systems of Difference Equations
Mathematics Department, Faculty of Education, Selcuk University, 42099, Konya, Turkey
Received 19 March 2008; Accepted 19 May 2008
Academic Editor: Bing Zhang
Copyright © 2008 İbrahim Yalçinkaya et al. 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
We show that every solution of the following system
of difference equations xn+1(1)=xn(2)/(xn(2)−1), xn+1(2)=xn(3)/(xn(3)−1),…,xn+1(k)=xn(1)/(xn(1)−1) as well as of the system xn+1(1)=xn(k)/(xn(k)−1), xn+1(2)=xn(1)/(xn(1)−1),…,xn+1(k)=xn(k−1)/(xn(k−1)−1) is periodic with period 2k if k ≠ 0 (mod2), and with period k if k=0 (mod2) where the initial values are nonzero real numbers for x0(1),x0(2),…,x0(k) ≠ 1.