Stević S.Iricanin, BratislavKosmala W.Smarda, Zdenek2023-02-082023-02-0820221025-5834https://scidar.kg.ac.rs/handle/123456789/16014We 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 xn+1= f(xn−l, xn−k) (Adv. Differ. Equ. 2018:447, 2018), is incorrect.article10.1186/s13660-022-02761-92-s2.0-85125487025