Öz
In this paper, we solve the following three-dimensional system of difference equations
xn=yn−4zn−5yn−1(an+bnzn−2xn−3yn−4zn−5),yn=zn−4xn−5zn−1(αn+βnxn−2yn−3zn−4xn−5),zn=xn−4yn−5xn−1(An+Bnyn−2zn−3xn−4yn−5), n∈N0,xn=yn−4zn−5yn−1(an+bnzn−2xn−3yn−4zn−5),yn=zn−4xn−5zn−1(αn+βnxn−2yn−3zn−4xn−5),zn=xn−4yn−5xn−1(An+Bnyn−2zn−3xn−4yn−5), n∈N0,where the sequences (an)n∈N0(an)n∈N0, (bn)n∈N0(bn)n∈N0, (αn)n∈N0(αn)n∈N0, (βn)n∈N0(βn)n∈N0, (An)n∈N0(An)n∈N0, (Bn)n∈N0(Bn)n∈N0 and the initial values x−j,y−jx−j,y−j, j=¯¯¯¯¯¯¯¯1,5j=1,5¯, are real numbers. In addition, the constant coefficient of the mentioned system is solved in closed form. Finally, we also describe the forbidden set of solutions of the system of difference equations.