Question 46
Let $N$ and $Z$ denote the sets of all positive integers and all integers, respectively. Find all functions $f: N \to Z$ such that:
$n$ divides $f(m)$ if and only if $m$ divides $\sum_{d|n} f(d)$, for all positive integers $n$ and $m$.
$n$ divides $f(m)$ if and only if $m$ divides $\sum_{d|n} f(d)$, for all positive integers $n$ and $m$.