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Omni-MATH / Let A be the set of all integers n such that 1≤n≤2021 and gcd(n,2021)=1. For every nonnegative integer j, let S(j)=∑_(n∈A)n^(j). Determine all values of j such that S(j) is a multi…

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problem

Let AA be the set of all integers nn such that 1≤n≤20211 \leq n \leq 2021 and gcd(n,2021)=1\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 2021.
Plain-text mathematical notation (without MathML)
Let A be the set of all integers n such that 1≤n≤2021 and gcd(n,2021)=1. For every nonnegative integer j, let
S(j)=∑_(n∈A)n^(j).
Determine all values of j such that S(j) is a multiple of 2021.
Original LaTeX notation
Let $A$ be the set of all integers $n$ such that $1 \leq n \leq 2021$ and $\gcd(n, 2021) = 1$. For every nonnegative integer $j$, let
\[S(j) = \sum_{n \in A} n^j.\]
Determine all values of $j$ such that $S(j)$ is a multiple of 2021.

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Source and history

task_id
8cdb5716-eaac-5796-9324-e214075763d9
task_key
test--8cdb5716-eaac-5796-9324-e214075763d9
task_revision_id
1
config / split
/ test

Official source

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