Erdős Problem #793

Erdős problem #793 · erdosproblems.com/793

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 $C$?

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Number Theory

Posed by

Paul Erdős

Year posed

1969

Years open

57y

Solved

2026-07

Model

GPT-5.6 Sol

Vendor

OpenAI

Collaborators

Przemek Chojecki

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

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Wikipedia

No dedicated article