Erdős Problem #303

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 $a,b,c$?

#303: [ErGr80,p.37]

number theory | unit fractions

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.

View the LaTeX source

This page was last edited 28 December 2025.

External data from the database - you can help update this
Formalised statement? Yes

1 comment on this problem

Likes this problem	None
Interested in collaborating	None
Currently working on this problem	None
This problem looks difficult	None
This problem looks tractable	None

When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #303, https://www.erdosproblems.com/303, accessed 2026-01-16