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APMO 2019 P5

Posted: Thu Aug 15, 2019 8:46 pm
by samiul_samin
Determine all the functions $f : \mathbb{R} \to \mathbb{R}$ such that
\[ f(x^2 + f(y)) = f(f(x)) + f(y^2) + 2f(xy) \]for all real numbers $x$ and $y$.