BdMC-Not So Easy II problem 5

[SANZEED]

Find all pairs of $(a,b)$ such that for all $n\in \mathbb{N}$,
$a\left \lfloor bn \right \rfloor=b\left \lfloor an \right \rfloor$

[*Mahi*]

Hint:

\[\frac ab = \frac {\left \lfloor na \right \rfloor}{\left \lfloor nb \right \rfloor} =\frac {\{na\}} {\{nb\}} \forall n\]
Where $\left \lfloor a \right \rfloor$ and $\{a\}$ are respectively floor and fractional part of $a$.