Fractional decomposition

Algebra Level 2

How many ordered pairs of integers \( (a,b) \) are there, such that \( 1 \leq a \leq 1000, 1 \leq b \leq 1000 \) and

\[ \frac{a}{b} = \frac{13}{31}? \]

Details and assumptions

For an ordered pair of integers \((a,b)\), the order of the integers matter. The ordered pair \((1, 2)\) is different from the ordered pair \((2,1) \).

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