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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

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

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by Arulx Z

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