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Find all functions

Source: Iran TST 2008

July 5, 2008
functionmodular arithmeticnumber theoryrelatively primefunctional equation

Problem Statement

k k is a given natural number. Find all functions f:N→N f: \mathbb{N}\rightarrow\mathbb{N} such that for each m,n∈N m,n\in\mathbb{N} the following holds: f(m)\plus{}f(n)\mid (m\plus{}n)^k
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