So Many Constraints!

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

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

where \([x]\) Is the Largest Integer Not Greater Than \(x\)

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

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