Question 43
Let $f: \mathbb{N} \to \mathbb{N}$ be a function such that for all positive integers $a$ and $b$,
$$
f(a) + f(b) - ab \mid af(a) + bf(b).
$$
Find all such functions $f$.
$$
f(a) + f(b) - ab \mid af(a) + bf(b).
$$
Find all such functions $f$.