Erdős Problem #336

Erdős problem #336 · erdosproblems.com/336

If $h(r)$ is the maximal finite exact order attainable by an additive basis of order at most $r$, what is $\lim_{r \to \infty} h(r)/r^2$? The candidate proof identifies the sharp limit $1/3$.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Additive Basis

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

—

Wikipedia

No dedicated article