An algebra problem by Miles Koumouris

Algebra Level 4

\[\large \begin{cases} a+b=n\\ \dfrac{1}{a}+\dfrac{1}{b}=\dfrac{-n}{896m(n+896m)} \end{cases} \]

Consider the system of equations above. If \(a-b=2016\), what is the maximum possible value of the product \(mn\)?

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