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Omni-MATH / Let S={1,2,…,2021}, and let F denote the set of functions f:S→S. For a function f∈F, let T_(f)={f²⁰²¹(s):s∈S} where f²⁰²¹(s) denotes f(f(⋯(f(s))⋯)) with 2021 copies of f. Compute t…

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problem

Let S={1,2,…,2021}S=\{1,2, \ldots, 2021\}, and let F\mathcal{F} denote the set of functions f:S→Sf: S \rightarrow S. For a function f∈Ff \in \mathcal{F}, let Tf={f2021(s):s∈S}T_{f}=\left\{f^{2021}(s): s \in S\right\} where f2021(s)f^{2021}(s) denotes f(f(⋯(f(s))⋯))f(f(\cdots(f(s)) \cdots)) with 2021 copies of ff. Compute the remainder when ∑f∈F|Tf|\sum_{f \in \mathcal{F}}\left|T_{f}\right| is divided by the prime 2017, where the sum is over all functions ff in F\mathcal{F}.
Plain-text mathematical notation (without MathML)
Let S={1,2,…,2021}, and let F denote the set of functions f:S→S. For a function f∈F, let T_(f)={f²⁰²¹(s):s∈S} where f²⁰²¹(s) denotes f(f(⋯(f(s))⋯)) with 2021 copies of f. Compute the remainder when ∑_(f∈F)|T_(f)| is divided by the prime 2017, where the sum is over all functions f in F.
Original LaTeX notation
Let $S=\{1,2, \ldots, 2021\}$, and let $\mathcal{F}$ denote the set of functions $f: S \rightarrow S$. For a function $f \in \mathcal{F}$, let $$T_{f}=\left\{f^{2021}(s): s \in S\right\}$$ where $f^{2021}(s)$ denotes $f(f(\cdots(f(s)) \cdots))$ with 2021 copies of $f$. Compute the remainder when $$\sum_{f \in \mathcal{F}}\left|T_{f}\right|$$ is divided by the prime 2017, where the sum is over all functions $f$ in $\mathcal{F}$.

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Source and history

task_id
591f854d-af83-56ba-b281-b92de34c1928
task_key
test--591f854d-af83-56ba-b281-b92de34c1928
task_revision_id
1
config / split
/ test

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