We consider the difference equation x_n+1= β_nx_n x_n-1, where {βn}xn=o is a positive periodic sequence with prime period k > 2. We completely determine the asymptotic behavior of every solution of this equation. In particular we show that every solution is periodic when 6 / k. Our results give necessary and sufficient conditions for the boundedness of all solutions of this equation. This solves one of the open problems proposed by E. Camouzis and G. Ladas in 3.
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