## 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 $x_{n+1}= \frac{A}{x_n}+ {1}{x_{n-2}},\quad n= 0,1,\ldots,$ 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; 10.1080/10236199608808079)].

### MSC:

 39A12 Discrete version of topics in analysis 39A10 Additive difference equations 39A30 Stability theory for difference equations
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