benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Determine all integers n≥2 with the following property: every n pairwise distinct integers whose sum is not divisible by n can be arranged in some order a₁,a₂,…,a_(n) so that n div…

Problem

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

problem

Determine all integers n≥2n\geqslant 2 with the following property: every nn pairwise distinct integers whose sum is not divisible by nn can be arranged in some order a1,a2,…,ana_1,a_2,\ldots, a_n so that nn divides 1⋅a1+2⋅a2+⋯+n⋅an.1\cdot a_1+2\cdot a_2+\cdots+n\cdot a_n. [i]Arsenii Nikolaiev, Anton Trygub, Oleksii Masalitin, and Fedir Yudin[/i]
Plain-text mathematical notation (without MathML)
Determine all integers n≥2 with the following property: every n pairwise distinct integers whose sum is not divisible by n can be arranged in some order a₁,a₂,…,a_(n) so that n divides 1⋅a₁+2⋅a₂+⋯+n⋅a_(n).

[i]Arsenii Nikolaiev, Anton Trygub, Oleksii Masalitin, and Fedir Yudin[/i]
Original LaTeX notation
Determine all integers $n\geqslant 2$ with the following property: every $n$ pairwise distinct integers whose sum is not divisible by $n$ can be arranged in some order $a_1,a_2,\ldots, a_n$ so that $n$ divides $1\cdot a_1+2\cdot a_2+\cdots+n\cdot a_n.$

[i]Arsenii Nikolaiev, Anton Trygub, Oleksii Masalitin, and Fedir Yudin[/i]

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
a8c55025-23ba-5818-8a17-4dac8d6de428
task_key
test--a8c55025-23ba-5818-8a17-4dac8d6de428
task_revision_id
1
config / split
/ test

Official source

initial import