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BALKAN-SL 2017 A3

Find all the functions f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} such that:

n+f(m)∣f(n)+nf(m)n+f(m) \mid f(n)+n f(m)

for any m,n∈Nm, n \in \mathbb{N}

Dataset text NuminaMath olympiads. Quoted with source.

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f(n)=n^{2} \text{ or } f(n)=1

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