Abstract
We present an example of a difference equation of arbitrary order, possessing the right-hand side function that is homogeneous to a certain degree and nonincreasing in each variable, which has a unique positive equilibrium, as well as solutions that do not converge to the equilibrium. The example shows that the main result in the paper: O. Moaaz, Dynamics of difference equation x_{n+1}=f(x_{n-l}, x_{n-k}) (Adv. Differ. Equ. 2018:447, 2018), is incorrect.
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