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Claim in Erdős problems named in new papers, 2026-10

A published paper or arXiv preprint answers the main question of Erdős Problem #272 (theorem erdos_272 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

Problem as stated at github.com/google-deepmind/formal-conjectures/blob/34ee0e3c5fd52d202d62a71094a37970cb5fb870/FormalConjectures/ErdosProblems/272.lean. The claim text is written by Corroborate; that site has not reviewed or endorsed it.

The problem, as stated in formal-conjectures (Apache 2.0):

Let N\geq 1. What is the largest t such that there are A_1,\ldots,A_t\subseteq \{1,\ldots,N\} with A_i\cap A_j a non-empty arithmetic progression for all i\neq j?

Verdict: no verdict yet

Evidence for

None yet.

Evidence against

None yet.

New papers that mention this problem