# Erdős Problem 456

A statement in qed.bot, the register of claims of AI work in mathematics. The register grades the evidence attached to each claim; it never rules on whether a proof is correct.

- Identifier: erdos:456
- Collection: Erdős
- Page: https://qed.bot/s/erdos-456
- Formal record: mixed; at its source: open
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://www.erdosproblems.com/456

## AI claims

### GPT-5.5 Pro, 4 May 2026

Candidate partial result (solutions to first part and second part; conditional solution to third part)

- Outcome: candidate
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V0: Claimed. No public artifact, or the claim is marked unverified at source.
- Fidelity F0: Absent. No formal statement is attached to the result.
- With: David Turturean
- Source: Erdős problems AI wiki, https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems

## Claimed on erdosproblems.com

Proof claims posted on erdosproblems.com, which says that listing a claim is no guarantee of proof correctness. Nobody has examined them, and none counts in the register's totals.

- David Turturean, using GPT-6-Astra Pro, earlier work: ChatGPT-5.5-Pro, Claude: a full proof claimed, 23 Sep 2026. Autonomy A?, evidence V0. https://www.erdosproblems.com/forum/thread/456/proof-claims#proof-claim-345

## Formal statements

- FormalConjectures/ErdosProblems/456.lean, https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/456.lean

Cite as: qed.bot, "Erdős Problem 456", https://qed.bot/s/erdos-456, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/