MathNet 2018-part-05 — 181 problems (EN–VI) Question 35

If $a, b \in [0, +\infty)$, $c \in \mathbb{R}$ and $\lfloor x \rfloor + \lfloor x + a \rfloor + \lfloor x + b \rfloor = \lfloor c x \rfloor$, for every $x \in \mathbb{R}$, prove that $\{a, b\} = \{\frac{1}{3}, \frac{2}{3}\}$ and $c = 3$.