Source labels openChecked July 26, 2026

Ben Green's Open Problem 16

What is the largest subset of $[N]$ with no solution to $x + 3y = 2z + 2w$ in distinct integers $x, y, z, w$ ?

Combinatorics AMS 5 AMS 11

Mathematical statement

What is the largest subset of $[N]$ with no solution to $x + 3y = 2z + 2w$ in distinct integers $x, y, z, w$ ?

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_16

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_16 (N : ℕ) :    ∃ A : Finset ℕ, A ⊆ Icc 1 N ∧ SolutionFree A ∧      A.card = answer(sorry) ∧      MaximalFor (fun B => B ⊆ Icc 1 N ∧ SolutionFree B) Finset.card A := 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 16background