On some solvable systems of difference equations

We show that the following systems of difference equations x(n+1) = u(n)/1 + v(n), y(n+1) = w(n)/1 + s(n), n is an element of N-0, where u(n), v(n), w(n), s(n) are some of the sequences x(n) or y(n), with real initial values x(0) and y(0), are solvable in fourteen out of sixteen possible cases. Two cases are left unsolved. Probably the most interesting is the result in the case u(n) = x(n), v(n) = x(n), w(n) = x(n), s(n) = y(n), where a fascinating formula is obtained in an elegant way by using some ad hoc ideas. (C) 2011 Elsevier Inc. All rights reserved.