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Zbl 1229.39018
Karatas, Ramazan
On solutions of the difference equation $x_{n+1}=\frac{(-1)^nx_{n-4}}{1+(-1)^nx_nx_{n-1}x_{n-2}x_{n-3}x_{n-4}}$.
(English)
[J] Selçuk J. Appl. Math. 8, No. 1, 51-56 (2007). ISSN 1302-7980

Summary: We study the solutions and attractivity of the difference equation $$x_{n+1}=\frac{(-1)^nx_{n-4}}{1+(-1)^nx_nx_{n-1} x_{n-2} x_{n-3} x_{n-4}}\,,\quad n=0,1,2,\dots$$ where $x_{-11},x_{-10},\dots,x_{-2},x{-1},x_0\in (0,\infty)$, and $x_0$ are real numbers such that $x_0x_{-1}x_{-2}x_{-3}x_{-4}\ne\pm 1$.
MSC 2000:
*39A20 Generalized difference equations
39A23

Keywords: rational difference equation; periodic solutions

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