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On the recursive sequence \(x_{n+1}=\frac A{x_n}+\frac 1{x_{n-2}}\). (English) Zbl 0904.39012
The authors establish that every positive solution of the equation \[ x_{n+1}= {A\over x_n}+ {1\over x_{n-2}},\quad n= 0,1,\dots, \] where \(x_{-1}\),\(x_{-2}\), \(A\in(0,\infty)\), converges to a period two solution. This proves Conjecture 2.4.2 of G. Ladas [J. Differ. Equ. Appl. 2, 449-452 (1996)].

MSC:
39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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