Question 41
Find all pairs $(a, b)$ of real numbers such that
$$
a \cdot \lfloor b \cdot n \rfloor = b \cdot \lfloor a \cdot n \rfloor
$$
for all positive integers $n$.
$$
a \cdot \lfloor b \cdot n \rfloor = b \cdot \lfloor a \cdot n \rfloor
$$
for all positive integers $n$.