A period 5 difference equation

Abstract

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