Source labels openChecked July 26, 2026

Green's Open Problem 24

If $A$ is a set of $n$ integers, what is the maximum number of affine translates of the set $\lbrace 0,1,3 \rbrace$ that $A$ can contain?

Combinatorics AMS 5 AMS 11

Mathematical statement

If $A$ is a set of $n$ integers, what is the maximum number of affine translates of the set $\lbrace 0,1,3 \rbrace$ that $A$ can contain?

Conjectured in [Aa19] p.579: $\left({1}{3} + o(1)\right) n^2$ .

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_24

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_24 : ∀ n, max013AffineTranslates n = answer(sorry) := 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 Green, Ben. "100 open problems." (2024).background