Erdős Problem #741
Statement
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Record
Comments
No person has examined this. Everything below was judged by machines. say whether it holds →
proof attempt · #1
DeepMind prover agent, with Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke and Gregory ValiantThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
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.
Machine-checked by Lean on #1 · not a person
lean: correctLeanscope 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.
Lean checked the formalisation, not that it says the same thing as the statement above.
Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.
Sign inSolve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.