MathDB
2022 Spring LMT Team 9

Source:

September 1, 2022
algebra

Problem Statement

Let r1,r2,...,r2021r_1, r_2, ..., r_{2021} be the not necessarily real and not necessarily distinct roots of x2022+2021x=2022x^{2022} + 2021x = 2022. Let Si=ri2021+2022riS_i = r_i^{2021}+2022r_i for all 1≤i≤20211 \le i \le 2021. Find ∣∑i=12021Si∣=∣S1+S2+...+S2021∣\left|\sum^{2021}_{i=1} S_i \right| = |S_1 +S_2 +...+S_{2021}|.
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