On a max-type and a min-type difference equation (Q732398)

The paper considers the positive solutions of \[ x_{n+1} = \max\left\{{{A_n}\over{x_n}},x_{n-2}\right\},\quad n\in N_0=\{n\in N:\;n\geq n_0\} \] and \[ x_{n+1} = \min\left\{{{A_n}\over{x_n}},x_{n-2}\right\},\quad n\in N_0 \] with \(n_0\in\{-k,\dots,-1,0,1,\dots\}\). If \(\{A_n\}_{n=0}^{\infty}\) is a positive sequence with period three, every positive solution of each equation above is periodic with period three.