benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Call admissible a set A of integers that has the following property:

Problem

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

problem

Call admissible a set AA of integers that has the following property: If x,y∈Ax,y \in A (possibly x=yx=y) then x2+kxy+y2∈Ax^2+kxy+y^2 \in A for every integer kk. Determine all pairs m,nm,n of nonzero integers such that the only admissible set containing both mm and nn is the set of all integers. [i]
Plain-text mathematical notation (without MathML)
Call admissible a set A of integers that has the following property:
If x,y∈A (possibly x=y) then x²+kxy+y²∈A for every integer k.
Determine all pairs m,n of nonzero integers such that the only admissible set containing both m and n is the set of all integers.

[i]
Original LaTeX notation
Call admissible a set $A$ of integers that has the following property:
If $x,y \in A$ (possibly $x=y$) then $x^2+kxy+y^2 \in A$ for every integer $k$.
Determine all pairs $m,n$ of nonzero integers such that the only admissible set containing both $m$ and $n$ is the set of all integers.

[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
ea0b504e-d60c-501d-b285-384355220b3f
task_key
test--ea0b504e-d60c-501d-b285-384355220b3f
task_revision_id
1
config / split
/ test

Official source

initial import