Erdős Problem #793

Precise statement

Let $F(n)$ be the largest $A\subseteq\{1,\dots,n\}$ with $a\nmid bc$ for distinct $a,b,c\in A$. Is $F(n)=\pi(n)+(C+o(1))\,n^{2/3}(\log n)^{-2}$ for some constant $C$?

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

GPT-5.6 Sol

GPT-5.6 Sol (prompted by Przemek Chojecki) proved $F(n)=\pi(n)+(\tfrac{27}{2}+o(1))\frac{n^{2/3}}{(\log n)^2}$, a refined form of Erdős's 1938 argument.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

Marked proved (Lean) on erdosproblems.com via a proof claim by GPT-5.6 Sol.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-07-01

   erdosproblems.com

   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.