All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 1199

Is it true that in any 2-colouring of N\mathbb{N} there exists an infinite set AA such that all elements of A+AA+A are the same colour?

Mathematical statement

Is it true that in any 2-colouring of N\mathbb{N} there exists an infinite set AA such that all elements of A+AA+A are the same colour?

A conjecture of Owings [Ow74].

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_1199

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_1199 :    answer(sorry)      (color :   Fin 2),  (A : Set ),    A.Infinite   n  (A+A),  m  (A+A), color n = color m := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References