On the eventual periodicity of xn+1 = max(1/xn, An/xn-1) with a period-five parameter

In this paper, we will study the max difference equation, x"n"+"1=max{1x"n,A"nx"n"-"1}, when {A"n} is a period-five sequence of real numbers greater than one. We will prove that every solution is eventually periodic with period twenty.