Question 24
Let $f$ be a real-valued function defined on the positive integers satisfying the following condition: For all $n \gt 1$ there exists a prime divisor $p$ of $n$ such that
$$
f(n) = f\left(\frac{n}{p}\right) - f(p)
$$
Given that $f(2001) = 1$, what is the value of $f(2002)$?
$$
f(n) = f\left(\frac{n}{p}\right) - f(p)
$$
Given that $f(2001) = 1$, what is the value of $f(2002)$?