Let
![\mathbb{N}_0](/media/m/c/c/3/cc3c4e1e85c27a8baf729520e3361526.png)
denote the set of nonnegative integers. Find all functions
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
from
![\mathbb{N}_0](/media/m/c/c/3/cc3c4e1e85c27a8baf729520e3361526.png)
to itself such that
%V0
Let $\mathbb{N}_0$ denote the set of nonnegative integers. Find all functions $f$ from $\mathbb{N}_0$ to itself such that
$$f(m + f(n)) = f(f(m)) + f(n)\qquad \text{for all} \; m, n \in \mathbb{N}_0.$$