Will you integrate it 2015 times? - IV

Calculus Level 3

A polynomial \(P : \mathbb{R} \rightarrow \mathbb{R} \) is of degree \(2015\). It is differentiated 2015 times to get \( Q(x) = \dfrac{ d^{2015} }{dx^{2015} } \big[ P(x) \big]\).

If the equation \( P(x) = Q(x) \) has \(n \) distinct roots, then what is the sum of all the possible values of \(n\)?


This problem is part of the set - Will you integrate it 2015 times? .
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