APMO 2019 P1

Discussion on Asian Pacific Mathematical Olympiad (APMO)
samiul_samin
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APMO 2019 P1

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