Problem

Source: 69 Polish MO 2018 Second Round - Problem 1

Tags: functional equation, algebra, Poland, function



Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ which satisfy conditions: $f(x) + f(y) \ge xy$ for all real $x, y$ and for each real $x$ exists real $y$, such that $f(x) + f(y) = xy$.