benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Determine which positive integers n have the following property: For all integers m that are relatively prime to n, there exists a permutation picolon {1,2,dots,n} to {1,2,dots,n} …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Determine which positive integers nn have the following property: For all integers mm that are relatively prime to nn, there exists a permutation $\pi\colon \{1,2,\dots,n\} \to \{1,2,\dots,n\}$ such that $\pi(\pi(k)) \equiv mk \pmod{n}$ for all k∈{1,2,…,n}k \in \{1,2,\dots,n\}.
Plain-text mathematical notation (without MathML)
Determine which positive integers n have the following property: For all integers m that are relatively prime to n, there exists a permutation $\pi\colon \{1,2,\dots,n\} \to \{1,2,\dots,n\}$ such that $\pi(\pi(k)) \equiv mk \pmod{n}$ for all k∈{1,2,…,n}.
Original LaTeX notation
Determine which positive integers $n$ have the following property: For all integers $m$ that are relatively prime to $n$, there exists a permutation $\pi\colon \{1,2,\dots,n\} \to \{1,2,\dots,n\}$ such that $\pi(\pi(k)) \equiv mk \pmod{n}$ for all $k \in \{1,2,\dots,n\}$.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
5c8d838d-3a6b-531b-830b-949ce2a15e1d
task_key
test--5c8d838d-3a6b-531b-830b-949ce2a15e1d
task_revision_id
1
config / split
/ test

Official source

initial import