benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Find the least positive integer N>1 satisfying the following two properties: There exists a positive integer a such that N=a(2a−1). The sum 1+2+⋯+(N−1) is divisible by k for every …

Problem

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

problem

Find the least positive integer N>1N>1 satisfying the following two properties: There exists a positive integer aa such that N=a(2a−1)N=a(2 a-1). The sum 1+2+⋯+(N−1)1+2+\cdots+(N-1) is divisible by kk for every integer 1≤k≤101 \leq k \leq 10.
Plain-text mathematical notation (without MathML)
Find the least positive integer N>1 satisfying the following two properties: There exists a positive integer a such that N=a(2a−1). The sum 1+2+⋯+(N−1) is divisible by k for every integer 1≤k≤10.
Original LaTeX notation
Find the least positive integer $N>1$ satisfying the following two properties: There exists a positive integer $a$ such that $N=a(2 a-1)$. The sum $1+2+\cdots+(N-1)$ is divisible by $k$ for every integer $1 \leq k \leq 10$.

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
5e9bfb91-c893-5559-a1d7-3699dfec0d99
task_key
test--5e9bfb91-c893-5559-a1d7-3699dfec0d99
task_revision_id
1
config / split
/ test

Official source

initial import