Closed form solution for $\left \lfloor{\frac{a}{x}}\right \rfloor$ = $\left \lfloor{\frac{b}{x}}\right \rfloor$?

Question

I need to find the smallest value of $x$ such that:

$\left \lfloor{\frac{a}{x}}\right \rfloor$ = $\left \lfloor{\frac{b}{x}}\right \rfloor$

EDIT: where $0 < x < a < b$, and $x \in \mathbb{N}$

Is there a closed-form solution for this problem? Any help or suggestions are greatly appreciated.

Thanks.