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• 1 Mansoura University Mathematics Department, Faculty of Science Mansoura 35516 Egypt
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In this paper we study the behavior of the difference equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x_{n + 1} = ax_{n - 2} + \frac{{bx_n x_{n - 2} }}{{cx_n + dx_{n - 3} }},n = 0,1,...$$ \end{document}
where the initial conditions x−3 , x−2 , x−1 , x0 are arbitrary positive real numbers and a, b, c, d are positive constants. Also, we give the solution of some special cases of this equation.

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