Aristotle
The solution was discovered autonomously by Aristotle and formalized in Lean; the human authors curated the exposition.
Provider: Harmonic · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Kourovka Problem 18.50 - Prescribed Permuted-Product Cardinality
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Given $n$ and $1 \le c \le n!$, can $n$ distinct group elements be chosen so that their $n!$ ordered products take exactly $c$ distinct values? Constructions realize every $c$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
Autonomously discovered and formally verified in Lean by Aristotle; author-curated arXiv preprint covering eight Kourovka Notebook problems.
Correctness: supported · statement fidelity: audited · peer review: none
Timeline
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arXiv:2607.17477 - On some problems from the Kourovka Notebook
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.