On fourteen solvable systems of difference equations

Abstract

In this paper, we mainly consider the systems of difference equationsxn+1=1+pnqn,yn+1=1+rnsn,n∈N0,where each of the sequences pn,qn,rn and sn represents either the sequence xn or the sequence yn, with nonzero real initial values x0 and y0. Then we solve fourteen out of sixteen possible systems. It is noteworthy to depict that the solutions are presented in terms of Fibonacci numbers for twelve systems of these fourteen systems.