# I'm invoking the Fractional-Part Function!

$\large{ \{q\}^2 = \left \{ \dfrac{n!}{2000} \right \} }$

How many pairs $$(n,q)$$ satisfy the above equation, where $$n$$ is a positive integer and $$q$$ is a non-integer rational number such that $$0<q<2000$$?

Notation: $$\{r\}$$ denotes the fractional part function.

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