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On the periodicity of the sequence \(x_{n+1} = \max\{\frac{A_0}{x_n},\frac{A_1}{x_{n-1}},\cdots,\frac{A_k}{x_{n-k}}\}\). (English) Zbl 0930.39011

The author gives a complete characterization of the sequence defined by \[ x_{n+1}=\max \left\{{A_0\over x_n},\dots,{A_k\over x_{n-k}} \right \}(n\geq k), \] when \(A_0<0,\dots,A_k<0\) solving an open problem of G. Ladas.

MSC:

39A11 Stability of difference equations (MSC2000)
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References:

[1] DOI: 10.1080/10236199608808067
[2] Amleh A.M., Computers and Math. with Appl.
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