Erdős Problem #796

Erdős problem #796 · erdosproblems.com/796

If $g_3(n)$ is the largest size of $A \subseteq [1,n]$ with fewer than three representations of every product $a_1 a_2$, does its conjectured second-order normalized term converge? The candidate proof gives an explicit limit constant.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Multiplicative Combinatorics

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-13

Model

GPT-5.6 starships (Claude Fable 5 reviewer)

Vendor

OpenAI / Anthropic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

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Wikipedia

No dedicated article