benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let n,m be positive integers. A set S of positive integers is called (n,m)-good, if: (1) m∈S; (2) for all a∈S, all divisors of a are also in S; (3) for all distinct a,b∈S, …

Problem

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

problem

Let n,mn, m be positive integers. A set SS of positive integers is called (n,m)(n, m)-good, if: (1) m∈Sm \in S; (2) for all a∈Sa\in S, all divisors of aa are also in SS; (3) for all distinct a,b∈Sa, b \in S, an+bn∈Sa^n+b^n \in S. For which (n,m)(n, m), the only (n,m)(n, m)-good set is N\mathbb{N}?
Plain-text mathematical notation (without MathML)
Let n,m be positive integers. A set S of positive integers is called (n,m)-good, if:

(1) m∈S;
(2) for all a∈S, all divisors of a are also in S;
(3) for all distinct a,b∈S, a^(n)+b^(n)∈S.

For which (n,m), the only (n,m)-good set is N?
Original LaTeX notation
Let $n, m$ be positive integers. A set $S$ of positive integers is called $(n, m)$-good, if:

(1) $m \in S$;
(2) for all $a\in S$, all divisors of $a$ are also in $S$;
(3) for all distinct $a, b \in S$, $a^n+b^n \in S$.

For which $(n, m)$, the only $(n, m)$-good set is $\mathbb{N}$?

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
9f8193ff-01b3-5ee9-a66f-329d7cdbd9bf
task_key
test--9f8193ff-01b3-5ee9-a66f-329d7cdbd9bf
task_revision_id
1
config / split
/ test

Official source

initial import