benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Determine the largest integer n such that there exist monic quadratic polynomials p₁(x),p₂(x),p₃(x) with integer coefficients so that for all integers i∈[1,n] there exists some …

Problem

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

problem

Determine the largest integer nn such that there exist monic quadratic polynomials p1(x),p2(x),p3(x)p_{1}(x), p_{2}(x), p_{3}(x) with integer coefficients so that for all integers i∈[1,n]i \in[1, n] there exists some j∈[1,3]j \in[1,3] and m∈Zm \in \mathbb{Z} such that pj(m)=ip_{j}(m)=i.
Plain-text mathematical notation (without MathML)
Determine the largest integer n such that there exist monic quadratic polynomials p₁(x),p₂(x),p₃(x) with integer coefficients so that for all integers i∈[1,n] there exists some j∈[1,3] and m∈Z such that p_(j)(m)=i.
Original LaTeX notation
Determine the largest integer $n$ such that there exist monic quadratic polynomials $p_{1}(x), p_{2}(x), p_{3}(x)$ with integer coefficients so that for all integers $i \in[1, n]$ there exists some $j \in[1,3]$ and $m \in \mathbb{Z}$ such that $p_{j}(m)=i$.

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
5f57c96b-f568-5034-bd69-de0d55c1f69b
task_key
test--5f57c96b-f568-5034-bd69-de0d55c1f69b
task_revision_id
1
config / split
/ test

Official source

initial import