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 statement3 of 4

This is still open even if $|I_2| = 1$ .

FormalConjectures/ErdosProblems/288.leanErdos288.erdos_288.variants.i2_card_eq_11 lineExact file

1sorry ↔ {(I, n₂) | I.1 ≤ I.2 ∧ ∃ n, ∑ n₁ ∈ (Set.Icc I.1 I.2).toFinset, (↑↑n₁)⁻¹ + (↑↑n₂)⁻¹ = ↑↑n}.Finite

OpenStatement only, no proof