# 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 \(n\)?