Source labels openChecked July 26, 2026

Ben Green's Open Problem 33

Are there infinitely many $q$ for which there is a set $A \subset \mathbb{Z}/q\mathbb{Z}$ , $|A| = (\sqrt{2} + o(1))q^{1/2}$ , with $A + A = \mathbb{Z}/q\mathbb{Z}$ ? [Gr24]

Combinatorics AMS 5 AMS 11

Mathematical statement

Are there infinitely many $q$ for which there is a set $A \subset \mathbb{Z}/q\mathbb{Z}$ , $|A| = (\sqrt{2} + o(1))q^{1/2}$ , with $A + A = \mathbb{Z}/q\mathbb{Z}$ ? [Gr24]

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_33

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_33 :    answer(sorry) ↔      ∀ ε : ℝ, 0 < ε →        ∃ᶠ q : ℕ+ in atTop,          ∃ A : Finset (ZMod q),            A + A = Finset.univ ∧            |((A.card : ℝ) / Real.sqrt q - Real.sqrt 2)| < ε := 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 33background