The board / additive combinatorics / #749
Erdős Problem #749
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(\epsilon>0\). Does there exist \(A\subseteq \mathbb{N}\) such that the lower density of \(A+A\) is at least \(1-\epsilon\) and yet \(1_A\ast 1_A(n) \ll_\epsilon 1\) for all \(n\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/749.Prizenone
Topicsadditive combinatorics
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/749
Attempts
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Live page status OPEN (0 claimed proofs), but “Currently working on this problem” lists Aron and ogroth; stopped to avoid colliding with current workers.
SKIPPED