Erdős problem 298

Does every set $A \subseteq \mathbb{N}$ of positive density contain some finite $S \subset A$ such that $\sum_{n \in S} \frac{1}{n} = 1$ ?

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

298.lean

Retained formal statement2 of 2

The literal natural-density interpretation of Erdős Problem 298 follows from [Bl21].

FormalConjectures/ErdosProblems/298.leanErdos298.erdos_298.variants.natural_density1 lineExact file

1True ↔ ∀ (A : Set ℕ), 0 ∉ A → A.HasPosDensity → ∃ S, ↑S ⊆ A ∧ ∑ n ∈ S, 1 / ↑n = 1

SolvedStatement only, no proof