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Found problems: 1

2022 IFYM, Sozopol, 4
Does there exist a surjective function $f:\mathbb{R} \rightarrow \mathbb{R}$ for which $f(x+y)-f(x)-f(y)$ takes only 0 and 1 for values for random $x$ and $y$?
function problem surjective function algebra functional equations probability