Source labels openChecked July 26, 2026

Ben Green's Open Problem 3

Suppose that $A \subset [0,1]$ is open and has measure greater than $\frac{1}{3}$ . Is there a solution to $xy = z$ with $x, y, z \in A$ ?

Number theory AMS 11

Mathematical statement

Suppose that $A \subset [0,1]$ is open and has measure greater than $\frac{1}{3}$ . Is there a solution to $xy = z$ with $x, y, z \in A$ ?

Statement source: Green's Open 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

green_3

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_3 :    answer(sorry) ↔ ∀ A : Set ℝ,      IsOpen A → A ⊆ Icc 0 1 → volume A > 1/3 →        ∃ x y z, x ∈ A ∧ y ∈ A ∧ z ∈ A ∧ x * y = z := 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

Pinned Formal Conjectures sourceformalization Ben Green's Open Problem 3background