# Is Newton Sums Relevant?

**Number Theory**Level 4

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 \[r_1^5+r_2^5+r_3^5+r_4^5+r_5^5\]