AT-OEMO-FED1 2019 Problem 4

Find all pairs $(a, b)$ of real numbers such that $a \cdot \lfloor b \cdot n\rfloor = b \cdot \lfloor a \cdot n \rfloor$ applies to all positive integers $n$ . (For a real number $x, \lfloor x\rfloor$ denotes the largest integer that is less than or equal to $x$ .)