benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Do there exist positive integers a₁<a₂<…<a₁₀₀ such that for 2≤k≤100, the least common multiple of a_(k−1) and a_(k) is greater than the least common multiple of a_(k) and a_(k+1)?

Problem

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

problem

Do there exist positive integers a1<a2<…<a100a_1<a_2<\ldots<a_{100} such that for 2≤k≤1002\le k\le100, the least common multiple of ak−1a_{k-1} and aka_k is greater than the least common multiple of aka_k and ak+1a_{k+1}?
Plain-text mathematical notation (without MathML)
Do there exist positive integers a₁<a₂<…<a₁₀₀ such that for 2≤k≤100, the least common multiple of a_(k−1) and a_(k) is greater than the least common multiple of a_(k) and a_(k+1)?
Original LaTeX notation
Do there exist positive integers $a_1<a_2<\ldots<a_{100}$ such that for $2\le k\le100$, the least common multiple of $a_{k-1}$ and $a_k$ is greater than the least common multiple of $a_k$ and $a_{k+1}$?

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
39ed3d4e-081f-5abd-b235-2bf5b6fd6f2d
task_key
test--39ed3d4e-081f-5abd-b235-2bf5b6fd6f2d
task_revision_id
1
config / split
/ test

Official source

initial import