Source labels openChecked July 26, 2026

Ben Green's Open Problem 60

Is there an absolute constant $c > 0$ such that, whenever $A ⊆ \mathbb{N}$ is a set of squares with $|A| ≥ 2$ , the sumset $A + A$ satisfies $|A + A| ≥ |A|^{1 + c}$ ?

Number theory AMS 11

Mathematical statement

Is there an absolute constant $c > 0$ such that, whenever $A ⊆ \mathbb{N}$ is a set of squares with $|A| ≥ 2$ , the sumset $A + A$ satisfies $|A + A| ≥ |A|^{1 + c}$ ?

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_60

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_60 :    answer(sorry) ↔ ∃ c > (0 : ℝ),      ∀ (A : Finset ℕ),        (∀ a ∈ A, IsSquare a) →        2 ≤ A.card →          ((A + A).card : ℝ) ≥ (A.card : ℝ) ^ (1 + c) := 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 60background