erdos_109

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].

theorem erdos_109 (A : Set ℕ) (h : A.upperDensity > 0) :
    ∃ B C : Set ℕ, B.Infinite ∧ C.Infinite ∧ B + C ⊆ A

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