Erdős Problem #741
Statement
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Context
A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.
People
Attempts
No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
From "Short proofs in combinatorics and number theory": "In each case, the proof is due entirely to an internal model at OpenAI. The role of the human authors was simply to digest the proofs and modify the write-ups for clarity and elegance." Priority note: this paper (31 March 2026) constructs the basis of order two with no syndetic split that Burr and Erdos asked for, which is this problem. The solve recorded here is dated 16 April 2026 and credited to a DeepMind prover agent, so the Lean-verified resolution appears to follow the earlier OpenAI-model proof rather than to be independent of it. Both are linked; the priority has not been adjudicated here.
Reviews
1 machine checkNo person has reviewed this attempt. 1 machine check below — a machine check is not human verification.
Machine check · not human verification
machine: correctscope Lean formalization of the result
Listed as solved on erdosproblems.com and the proof is verified in Lean. Solve credited via Terence Tao's AI-contributions wiki.
No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.
Discussion of this attempt
no comments
Solve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.
Discussion
Nothing has been said about this problem yet.
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