On the Recursive Sequence +=max{,}/−

We investigate the periodic nature of the solution of the max-type difference equation +1=max{,}/2−1, =0,1,2,…, where the initial conditions are −1=1 and 0=2 for ∈(0,∞), and that 1 and 2 are positive rational numbers. The results in this paper solve the Open Problem proposed by Grove and Ladas (2005)