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Functional equation

Source: BMO 2009 Problem 4

April 30, 2009
functioninductionalgebra proposedalgebra

Problem Statement

Denote by S S the set of all positive integers. Find all functions f:S→S f: S \rightarrow S such that f (f^2(m) \plus{} 2f^2(n)) \equal{} m^2 \plus{} 2 n^2 for all m,n∈S m,n \in S.
Bulgaria
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