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On the max-type equation \(x_{n+1}=\max \{\frac{A}{x_n},x_{n-2}\}\). (English) Zbl 1169.39003
Authors’ summary: We show that every well-defined solution of the difference equation
\[ x_{n+1}= \max\left\{\frac{A}{x_n},x_{n-2}\right\},\;n\in\mathbb{N}_0, \] where \(A\in\mathbb{R}\), is eventually periodic with period three.

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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