So Many Constraints!

Number Theory Level 5

Let (a,b)(a,b) are positive integers such that

{gcd⁡(a,b)=1,b≤100,(ab−[ab])[ab]=2013,\begin{cases} \gcd(a,b)=1, \\ b\le 100, \\ \left(\dfrac{a}{b}-\left[\dfrac{a}{b}\right]\right)\left[\dfrac{a}{b}\right]=2013, \end{cases}

where [x][x] Is the Largest Integer Not Greater Than xx

Find the total number of pairs (a,b)(a,b).

Gabriel Merces by Gabriel Merces
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