On the positive solutions of the system of rational difference equations xn+1 = 1/yn−k, yn+1 = yn/xn−myn−m−k

Our aim in this paper is to investigate the periodic nature of solutions of the system of rational difference equations xn+1 = 1/yn−k, yn+1 = yn/xn−myn−m−k, n= 0, 1, . . . , where k is a nonnegative integer, m is a positive integer and the initial values x−m, x−m+1, . . . , x0, y−m−k, y−m−k+1, . . . , y0 are positive real numbers. © 2005 Elsevier Inc. All rights reserved.