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integer functions

Source: Korean MO 1994

March 11, 2008
functionalgebra unsolvedalgebra

Problem Statement

Let S S be the set of nonnegative integers. Find all functions f,g,h:S→S f,g,h: S\rightarrow S such that f(m\plus{}n)\equal{}g(m)\plus{}h(n), for all m,n∈S m,n\in S, and g(1)\equal{}h(1)\equal{}1.
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