# Yay for 2014! #6

Algebra Level 5

Let $$r_{1}, r_{2}, ..., r_{2014}$$ be the complex roots, not all necessarily distinct, of the polynomial $$x^{2014}+2014x^{2013}-1$$. If

$S = \sum_{n=1}^{2014}\sum_{k=1}^{2014}r_{k}^{n},$

and $$\frac{2015}{2014}S = a^{2014} + b$$, for some positive integers $$a$$ and $$b$$ such that $$a$$ is as large as possible, find the units digit of $$a + b + 2014.$$

This problem is part of the set Yay for 2014!.

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