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Erdős problem 288

Is it true that there are only finitely many pairs of intervals I1I_1, I2I_2 such that n1I11n1+n2I21n2N? \sum_{n_1 \in I_1} \frac{1}{n_1} + \sum_{n_2 \in I_2} \frac{1}{n_2} \in \mathbb{N}?

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