The board / number theory / #303
Erdős Problem #303
PROVED LEANdatabase updated 2025-12-21
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \(a, b, c\)? This is true, as proved by Brown and Rödl [BrRo91]. This was formalized in Lean by Yuan using Seed-Prover.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/303.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/303
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.