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Find all functions

Source: Balkan MO 2000, problem 1 and 1997, problem 4 (!!)

October 16, 2005
algebrafunctional equationBalkan Mathematics Olympiad

Problem Statement

Find all functions f:R→Rf: \mathbb R \to \mathbb R such that f(xf(x)+f(y))=f2(x)+y f( xf(x) + f(y) ) = f^2(x) + y for all x,y∈Rx,y\in \mathbb R.
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