BALKAN-SL 2017 A3

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

$n+f(m) \mid f(n)+n f(m)$

for any $m, n \in \mathbb{N}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

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

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