Question 8
A8 (ROM) IMO3 Let $\mathbb N_0$ denote the set of nonnegative integers. Find all functions $f$ from $\mathbb N_0$ into itself such that
$$f(m+f(n))=f(f(m))+f(n),\qquad\forall m,n\in\mathbb N_0.$$
$$f(m+f(n))=f(f(m))+f(n),\qquad\forall m,n\in\mathbb N_0.$$