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Algebra Difficulty 4.8 AIME Prove it Belarus

Find all functions f:N→Nf: \mathbb{N} \to \mathbb{N}, such that mf(m)+nmf(m) + n is divisible by m2+f(n)m^2 + f(n) for all m,n∈Nm, n \in \mathbb{N}.

Solution

### 2. See IMO-2013 Shortlist, Problem N1.

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