The board / number theory / #288
Erdős Problem #288
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is it true that there are only finitely many pairs of intervals \(I_1\), \(I_2\) such that \[ \sum_{n_1 \in I_1} \frac{1}{n_1} + \sum_{n_2 \in I_2} \frac{1}{n_2} \in \mathbb{N}? \]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/288.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/288
Attempts
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The live page status is OPEN, but it lists Rafikzeraoulia2025 and Ritvik_Nayak as currently working on Erdős problem #288, so the mandatory no-collision rule applies.
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