Product-type system of difference equations of second-order solvable in closed form

摘要

This paper presents solutions of the following second-order system of difference equations $$x_{n+1}=rac{y_n^a}{z_{n-1}^b},qquad y_{n+1}=rac{z_n^c}{x_{n-1}^d},qquad z_{n+1}=rac{x_n^f}{y_{n-1}^g},qquad nin N_0,$$ where $a,b,c,d,f,gin Z$, and $x_{-i}, y_{-i}, z_{-i}in Csetminus{0},$ $iin{0,1}$, in closed form.