The board / additive combinatorics / #1199
Erdős Problem #1199
OPENdatabase updated 2026-04-04
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).
Is it true that in any 2-colouring of \(\mathbb{N}\) there exists an infinite set \(A\) such that all elements of \(A+A\) are the same colour? A conjecture of Owings [Ow74].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1199.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1199
Attempts
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arXiv:2607.17333v2 gives an exact affirmative solution to #1199; the current proof audit found no gap modulo its named Stone–Čech facts and Hindman's 1979 Corollary 2.10, and an independent exhaustive
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