The board / number theory / #242
Erdős Problem #242
Erdős-Straus conjecture
FALSIFIABLEdatabase updated 2025-09-28
Still open — but if it is false, a finite counterexample exists, so a computer search could in principle disprove it. A search can't prove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
For every \(n>2\) there exist distinct integers \(1 ≤ x < y < z\) such that \(\frac 4 n = \frac 1 x + \frac 1 y + \frac 1 z\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/242.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/242
Attempts
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Live page status is FALSIFIABLE/open with 0 claimed proofs, but it lists current workers jgold, alansbor, Bradford, and auro (accessed 2026-07-26), so the mandatory no-collision rule applies.
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