Just Throw In Some Exponents

Number Theory Level 3

$\dfrac { { a }^{ 3 } }{ { b }^{ 2 } } =\dfrac { 3 }{ 16 }$ If all the $$n$$ pairs of positive integers $$(a,b)$$ that satisfy the equation above, where $$a<100$$, are

$(a_1 ,b_1) , (a_2, b_2) , \ldots , (a_n, b_n) ,$

submit your answer as $$\displaystyle \sum_{i=1}^n \dfrac{b_i}{a_i}$$.

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