Question 36
Let $f: \mathbb{N} \rightarrow \mathbb{N}$ be an injective function such that $f(1)=2$, $f(2)=4$ and
$$
f(f(m)+f(n))=f(f(m))+f(n)
$$
for all $m, n \in \mathbb{N}$. Prove that $f(n)=n+2$ for all $n \geq 2$.
$$
f(f(m)+f(n))=f(f(m))+f(n)
$$
for all $m, n \in \mathbb{N}$. Prove that $f(n)=n+2$ for all $n \geq 2$.