A period 5 difference equation

The main goal of this note is to introduce another second-order difference equation where every nontrivial solution is of minimal period 5, namely the difference equation: xn+1 = 1 + xn?1 xnxn?1 ? 1, n = 1, 2, 3, . . . with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.