Erdős problem 741 · problems.science

Let $A\subseteq \mathbb{N}$ be such that $A+A$ has positive density in the literal sense that its natural density exists and is positive. Can one always decompose $A=A_1\sqcup A_2$ such that $A_1+A_1$ and $A_2+A_2$ both have positive density in this sense?

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Browse retained paths and inspect the exact material available for this Problem.

4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

741.lean

Retained formal statement4 of 4

Let $A\subseteq \mathbb{N}$ be such that $A+A$ has positive lower density. Can one always decompose $A=A_1\sqcup A_2$ such that $A_1+A_1$ and $A_2+A_2$ both have positive lower density?

FormalConjectures/ErdosProblems/741.leanErdos741.erdos_741.variants.lower4 linesExact file

1True ↔2  ∀ (A : Set ℕ),3    0 < (A + A).lowerDensity →4      ∃ A₁ A₂, A = A₁ ∪ A₂ ∧ Disjoint A₁ A₂ ∧ 0 < (A₁ + A₁).lowerDensity ∧ 0 < (A₂ + A₂).lowerDensity

OpenStatement only, no proof

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