erdos_288

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

theorem erdos_288 : answer(sorry) ↔ Set.Finite { I : Fin 2 → ℕ+ × ℕ+ |
    ∀ j, (I j).1 ≤ (I j).2 ∧
      ∃ n : ℕ+, (∑ j : Fin 2, ∑ nⱼ ∈ Set.Icc (I j).1 (I j).2, (nⱼ⁻¹ : ℚ)) = n }

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