A period ۵ difference equation

The main goal of this note is to introduce another second-order difference equation where every nontrivial solution is of minimal period ۵, namely the difference equation:x_{n+۱} =\frac{۱ + x_{n−۱}}{x_nx_{n−۱} − ۱},      n = ۱, ۲, ۳, . . .with initial conditions x_۰ and x_۱ any real numbers such that x_۰x_۱ \neq ۱.

Keywords:

difference equation , periodicity , equilibrium points , convergence