Is it true that, for all sufficiently large $k$, there exists finite intervals
$I_1, \dotsc, I_k \subset \mathbb{N}$ with $|I_i| \geq 2$ for $1 \leq i \leq k$ such that
$$
1 = \sum_{i=1}^k \sum_{n \in I_i} \frac{1}{n}.
$$
Actions
Submit a Proof
Have a proof attempt? Submit it for zero-trust verification.
theorem erdos_289 : answer(sorry) ↔
(∀ᶠ k : ℕ in atTop, ∃ I : Fin k → ℕ × ℕ,
(∀ i, (I i).1 < (I i).2) ∧
(∀ i j, i ≠ j → (I i).2 < (I j).1 ∨ (I j).2 < (I i).1) ∧
∑ i, ∑ n ∈ .Icc (I i).1 (I i).2, (n⁻¹ : ℚ) = 1)
