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On some solvable systems of difference equations. (English) Zbl 1253.39011
The author studies the following system of difference equations $x_{n+1}=\frac{u_n}{1+v_n}, \qquad y_{n+1}=\frac {w_n}{1+s_n}, \qquad n\in \mathbb{N}_0,$ where $$u_n$$, $$v_n$$, $$w_n$$, $$s_n$$ are some of the sequences $$x_n$$ or $$y_n$$, with real initial values $$x_0$$ and $$y_0$$. For fourteen of the sixteen possible cases, the author obtains the general solutions. The unsolved cases are $x_{n+1}=\frac{y_n}{1+y_n}, \qquad y_{n+1}=\frac{y_n}{1+x_n}, \qquad n\in \mathbb{N}_0$ and the symmetric counterpart $x_{n+1}=\frac {x_n}{1+y_n}, \qquad y_{n+1}=\frac{x_n}{1+x_n}, \qquad n\in \mathbb{N}_0.$

##### MSC:
 39A20 Multiplicative and other generalized difference equations
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##### References:
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