Question 38
Let $f: \mathbb{N} \to \mathbb{N}_0$ be a function that satisfies
$$
f(mn) = mf(n) + nf(m)
$$
for all positive integers $m, n$ and $f(2024) = 10120$.
Prove that there are two integers $m, n$ with $m \neq n$ such that $f(m) = f(n)$.
$$
f(mn) = mf(n) + nf(m)
$$
for all positive integers $m, n$ and $f(2024) = 10120$.
Prove that there are two integers $m, n$ with $m \neq n$ such that $f(m) = f(n)$.