Question 4
Let $\mathbb N$ be the set of positive integers, that is, $\mathbb N=\{1,2,\ldots\}$. Find all functions $f:\mathbb N\to\mathbb N$ such that
$$f(f(m)+f(n))=m+n\qquad\text{for all }m,n\in\mathbb N.$$
$$f(f(m)+f(n))=m+n\qquad\text{for all }m,n\in\mathbb N.$$