The board / number theory / #302
Erdős Problem #302
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).
A finite set \(A\) of positive integers admits no solution to \(\frac{1}{a} = \frac{1}{b} + \frac{1}{c}\) with \(a, b, c\) distinct elements of \(A\).
\(f N\) is the size of the largest \(A ⊆ \{1, …, N\}\) containing no solution to \(\frac{1}{a} = \frac{1}{b} + \frac{1}{c}\) with distinct \(a, b, c ∈ A\).
Let \(f(N)\) be the size of the largest \(A\subseteq \{1,\ldots,N\}\) such that there are no solutions to \[\frac{1}{a}= \frac{1}{b}+\frac{1}{c}\] with distinct \(a,b,c\in A\)? Estimate \(f(N)\). The colouring version of this is [303], which was solved by Brown and Rödl [BrRo91].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 5 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/302.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA390395
Original pageerdosproblems.com/302
Attempts
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Live page status OPEN; it lists 1 claimed proof (partial, attributed to Robert Schuh using GPT 5.6 and Kimi 2.6, submitted 2026-07-20 by 15Redstones) and CURRENTLY WORKING markers for Woett and Quanyu
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