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On the recursive sequence $$x_{n+1}=A+x_{n}^{p}/x_{n-1}^{p}$$. (English) Zbl 1180.39007
Summary: This paper studies the boundedness, global attractivity, and periodicity of the positive solutions of the difference equation $$x_{n+1}=A+x_n^p/x_{n-1}^p$$, $$n\in\mathbb N_0$$, with $$p,A\in(0,\infty)$$. The main results give a complete picture regarding the boundedness character of the positive solutions of the equation.