Newton or Vieta?

Algebra Level 4

Let $r_1$, $r_2$, $r_3$, ..., and $r_{20}$ be the roots of the equation $z^{20}-19z+2=0$.

Find

$r_1^{20}+r_2^{20}+r_3^{20}+\dots+r_{20}^{20}$

×