# 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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