# Is Newton Sums Relevant?

A degree $5$ monic polynomial $P(x)$ has $5$ (not necessarily distinct) integer roots. Given that $P(0)=2014$, how many ordered quintuplets of roots $(r_1,r_2,r_3,r_4,r_5)$ satisfy the property that $r_1+r_2+r_3+r_4+r_5$ has the same units digit as $r_1^5+r_2^5+r_3^5+r_4^5+r_5^5$

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