Erdős problem 109 · problems.science

Any $A\subseteq \mathbb{N}$ of positive upper density contains a sumset $B+C$ where both $B$ and $C$ are infinite.

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1 retained statement2415f78e850a

FormalConjectures/ErdosProblems/

109.lean

Retained formal statement1 of 1

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].

FormalConjectures/ErdosProblems/109.leanErdos109.erdos_1091 lineExact file

1∀ (A : Set ℕ), A.upperDensity > 0 → ∃ B C, B.Infinite ∧ C.Infinite ∧ B + C ⊆ A

SolvedStatement only, no proof