Problem

Source: Kazakhstan MO 2018 final round.Grade 11;Problem 3

Tags: function, algebra, Kazakhstan



Is there exist a function $f:\mathbb {N}\to \mathbb {N}$ with for $\forall m,n \in \mathbb {N}$ $$f\left(mf\left(n\right)\right)=f\left(m\right)f\left(m+n\right)+n ?$$