An algebra problem by Govind Ramesh

Algebra Level 5

\[\dfrac{3^2 + 1}{3^2 - 1} + \dfrac{5^2 + 1}{5^2 - 1}+ \cdots + \dfrac{99^2 + 1}{99^2 - 1}\]

The above sum can be written as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers.

Find the number of number of positive divisors of \(a\) and of \(b\) separately. Then enter your answer as the sum of these 2 numbers.

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