FormalConjectures.ErdosProblems.«109»

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import FormalConjecturesUtil

Erdős Problem 109

References:

erdosproblems.com/109

[MRR19] J. Moreira, F.K. Richter, and D. Robertson, A proof of a sumset conjecture of Erdős, Annals of Math. 189 (2019), 605-652.


open Pointwise


namespace Erdos109

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].

@[category research solved, AMS 5]
theorem declaration uses 'sorry'erdos_109 (A : Set ℕ) (h : A.upperDensity > 0) :
    ∃ B C : Set ℕ, B.Infinite ∧ C.Infinite ∧ B + C ⊆ A := byA:Set ℕh:A.upperDensity > 0⊢ ∃ B C, B.Infinite ∧ C.Infinite ∧ B + C ⊆ A
  sorryAll goals completed! 🐙


end Erdos109