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Functional equation

Source: Kazakhstan NMO 2005 (Final round) P4

December 16, 2014
functionalgebra proposedalgebraKazakhstan

Problem Statement

Find all functions f:Rā†’Rf :\mathbb{R}\to\mathbb{R}, satisfying the condition
f(f(x)+x+y)=2x+f(y)f(f(x)+x+y)=2x+f(y)
for any real xx and yy.
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