Question 38
We are given the function $f: \mathbb{Z}_{\gt 0} \rightarrow \mathbb{Z}$ satisfying the properties:
(i) $f(p)=1$ for all prime numbers $p$,
(ii) $f(x y)=y f(x)+x f(y)$ for all $x, y \in \mathbb{Z}_{\gt 0}$.
Determine the smallest $n \geq 2016$ with $f(n)=n$.
(i) $f(p)=1$ for all prime numbers $p$,
(ii) $f(x y)=y f(x)+x f(y)$ for all $x, y \in \mathbb{Z}_{\gt 0}$.
Determine the smallest $n \geq 2016$ with $f(n)=n$.