The board / number theory / #532
Erdős Problem #532
PROVED LEANdatabase updated 2026-01-31
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).
If \(\mathbb{N}\) is 2-coloured then is there some infinite set \(A\subseteq \mathbb{N}\) such that all finite subset sums\[ \sum_{n\in S}n\](as \(S\) ranges over all non-empty finite subsets of \(A\)) are monochromatic? Asked by Graham and Rothschild. Proved by Hindman [Hi74] (for any number of colours).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/532.Prizenone
Topicsnumber theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/532
Attempts
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