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f(m)+f(n)|m+n - Iran NMO 2004 (Second Round) - Problem4

Source:

September 24, 2010
functioninductionnumber theoryprime numbersnumber theory proposed

Problem Statement

N\mathbb{N} is the set of positive integers. Determine all functions f:N→Nf:\mathbb{N}\to\mathbb{N} such that for every pair (m,n)∈N2(m,n)\in\mathbb{N}^2 we have that: f(m)+f(n) ∣ m+n.f(m)+f(n) \ | \ m+n .
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