Advances in Difference Equations
Volume 2008 (2008), Article ID 143943, 9 pages
Research Article

On the Solutions of Systems of Difference Equations

İbrahim Yalçinkaya, Cengiz Çinar, and Muhammet Atalay

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.


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(k1)/(xn(k1)1) is periodic with period 2k if k0 (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.