Question 31
Let $f: \mathbb{Z}_{\gt 0} \to \mathbb{Z}$ be a function with the following properties:
(i) $f(1) = 0$,
(ii) $f(p) = 1$ for all prime numbers $p$,
(iii) $f(xy) = y f(x) + x f(y)$ for all $x, y$ in $\mathbb{Z}_{\gt 0}$.
Determine the smallest integer $n \ge 2015$ that satisfies $f(n) = n$.
(i) $f(1) = 0$,
(ii) $f(p) = 1$ for all prime numbers $p$,
(iii) $f(xy) = y f(x) + x f(y)$ for all $x, y$ in $\mathbb{Z}_{\gt 0}$.
Determine the smallest integer $n \ge 2015$ that satisfies $f(n) = n$.