Problem Statement
Is it true that in any finite colouring of the integers there exists a monochromatic solution to\[\frac{1}{a}=\frac{1}{b}+\frac{1}{c}\]with distinct $a,b,c$?
Categories:
Number Theory Unit Fractions
Progress
The density version of this is [302]. This colouring version is true, as proved by Brown and Rödl [BrRo91].This problem has been formalised in Lean as part of the Google DeepMind Formal Conjectures project.
Source: erdosproblems.com/303 | Last verified: January 14, 2026