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a+b+c|f(a)+f(b)+f(c)

Source: Iranian National Olympiad (3rd Round) 2008

August 31, 2008
algebrapolynomialmodular arithmeticfunctionnumber theory proposednumber theory

Problem Statement

Find all polynomials f∈Z[x] f\in\mathbb Z[x] such that for each a,b,x∈N a,b,x\in\mathbb N a\plus{}b\plus{}c|f(a)\plus{}f(b)\plus{}f(c)
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