On the positive solutions of the system of rational difference equations xn+1=1/yn−kxn+1=1/yn−k, yn+1=yn/xn−myn−m−kyn+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 equationsxn+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−mx−m, x−m+1x−m+1, …, x0x0, y−m−ky−m−k, y−m−k+1y−m−k+1, …, y0y0 are positive real numbers.