An algebra problem by Aditya Moger

Algebra Level 4

\[ \begin{align} a & = \dfrac{1^2}1 + \dfrac{2^2}3 + \dfrac{3^2}5 + \cdots + \dfrac{1001^2}{2001} \\ b & = \dfrac{1^2}3 + \dfrac{2^2}5 + \dfrac{3^2}7 + \cdots + \dfrac{1001^2}{2003} \end{align} \]

For \(a\) and \(b\) as defined above, find the integer closest to \(a-b\).

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