Question 27
Let $\mathbb{Z}_{ \gt 0}$ be the set of positive integers. Determine all functions $f\colon \mathbb{Z}_{ \gt 0} \to \mathbb{Z}$ such that for every $n \in \mathbb{Z}_{ \gt 0}$, and every positive divisor $d$ of $n$, there exists a positive divisor $e$ of $n$ such that $n$ divides $d + f(e)$.