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Putnam 2021 A5

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December 5, 2021
PutnamPutnam 2021

Problem Statement

Let AA be the set of all integers nn such that 1≤n≤20211 \le n \le 2021 and gcd(n,2021)=1\text{gcd}(n,2021)=1. For every nonnegative integer jj, let S(j)=∑n∈Anj. S(j)=\sum_{n \in A}n^j. Determine all values of jj such that S(j)S(j) is a multiple of 20212021.
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