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The global attractivity of the rational difference equation $$y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}$$. (English) Zbl 1131.39006
For the equation in the title with $$0< k< m$$ it is shown that all positive solutions converge to the equilibrium 1. Two conjectures concerning the asymptotic stability for positive solutions of more general difference equations are given.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations
##### Keywords:
asymptotic stability; symmetry; positive solutions
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##### References:
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