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function from VietNam

Source: VietNam TST 2004, problem 2

May 9, 2004

functioncalculusintegrationsearchalgebra unsolvedalgebra

Problem Statement

Find all real values of

\alpha

, for which there exists one and only one function

f: \mathbb{R} \mapsto \mathbb{R}

and satisfying the equation

f(x^2 + y + f(y)) = (f(x))^2 + \alpha \cdot y

for all

x, y \in \mathbb{R}