The board / additive combinatorics / #109
Erdős Problem #109
Erdős sumset conjecture
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Any \(A\subseteq \mathbb{N}\) of positive upper density contains a sumset \(B+C\) where both \(B\) and \(C\) are infinite. The Erdős sumset conjecture. Proved by Moreira, Richter, and Robertson [MRR19].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/109.Prizenone
Topicsadditive combinatorics
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/109
Attempts
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