MathNet 2019-part-01 — 184 problems (EN–VI) Question 20

Let $\mathbb{Z}^{+}$ be the set of positive integers. Determine all functions $f: \mathbb{Z}^{+} \rightarrow \mathbb{Z}^{+}$ such that $a^{2} + f(a) f(b)$ is divisible by $f(a) + b$ for all positive integers $a$ and $b$.