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Erdős problem 1090

Let k≥3k\geq 3. Does there exist a finite set A⊂R2A\subset \mathbb{R}^2 such that, in any 22-colouring of AA, there exists a line which contains at least kk points from AA, and all the points of AA on the line have the same colour?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/1090.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1090.leanErdos1090.erdos_10909 linesExact file
True ↔  ∀ (k : ℕ),    3 ≤ k →      ∃ A,        ∀ (C : ↥A → Fin 2),          ∃ S,            ∃ (hSA : S ⊆ A),              Collinear ℝ ↑S ∧                S.card ≥ k ∧ (∀ y ∈ A, y ∈ affineSpan ℝ ↑S → y ∈ S) ∧ ∃ c, ∀ (x : Fin 2 → ℝ) (hx : x ∈ S), C ⟨x, ⋯⟩ = c
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:1090
  • PLBY Lean proofsErdosProblems.Erdos1090

Reported activity

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  • AI building on literature

    Erdős AI contributions wiki · 27 Feb, 2026

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    Aristotle, Gemini 3 Flash
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