Erdős problem 288

Is it true that there are only finitely many pairs of intervals $I_1$ , $I_2$ such that $\sum_{n_1 \in I_1} \frac{1}{n_1} + \sum_{n_2 \in I_2} \frac{1}{n_2} \in \mathbb{N}?$

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

288.lean

Retained formal statement4 of 4

It is perhaps true with two intervals replaced by any $k$ intervals.

FormalConjectures/ErdosProblems/288.leanErdos288.erdos_288.variants.k_intervals3 linesExact file

1sorry ↔2  ∀ (k : ℕ),3    {I | ∀ (j : Fin k), (I j).1 ≤ (I j).2 ∧ ∃ n, ∑ j, ∑ nⱼ ∈ (Set.Icc (I j).1 (I j).2).toFinset, (↑↑nⱼ)⁻¹ = ↑↑n}.Finite

OpenStatement only, no proof