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Problem 5 of Fourth round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018
functional equationalgebra

Problem Statement

Find all functions f:[0,+∞)→[0,+∞)f :[0, +\infty) \rightarrow [0, +\infty) for which
f(f(x)+f(y))=xyf(x+y)f(f(x)+f(y)) = xy f (x+y)
for every two non-negative real numbers xx and yy.
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