Advances in Difference Equations
Volume 2008 (2008), Article ID 143943, 9 pages
doi:10.1155/2008/143943

On the solutions of systems of difference equations

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.