erdos_298

Does every set $A \subseteq \mathbb{N}$ of positive density contain some finite $S \subset A$ such that $\sum_{n \in S} \frac{1}{n} = 1$? The answer is yes, proved by Bloom [Bl21]. [Bl21] Bloom, T. F., _On a density conjecture about unit fractions_. arXiv:2112.03726 (2021). Note: The solution to this problem has been formalized in Lean 3 by T. Bloom and B. Mehta, see https://github.com/b-mehta/unit-fractions

theorem erdos_298 : answer(True) ↔ (∀ (A : Set ℕ), 0 ∉ A → A.HasPosDensity →
    ∃ (S : Finset ℕ), ↑S ⊆ A ∧ ∑ n ∈ S, (1 / n : ℚ) = 1)

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