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Let r1r_1r1, r2r_2r2, r3r_3r3, ..., and r20r_{20}r20 be the roots of the equation z20−19z+2=0z^{20}-19z+2=0z20−19z+2=0.
Find
r120+r220+r320+⋯+r2020r_1^{20}+r_2^{20}+r_3^{20}+\dots+r_{20}^{20}r120+r220+r320+⋯+r2020
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