Green's Open ProblemsCombinatorics
Ben Green's Open Problem 37
Given a natural number N, what is the smallest size of a subset of ℕ that contains, for each d = 1, …, N, an arithmetic progression of length k with common difference d.
Mathematical statement
Given a natural number N, what is the smallest size of a subset of ℕ that contains, for each d = 1, …, N,
an arithmetic progression of length k with common difference d.
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_37
theorem green_37 (N k : ℕ) : IsLeast { m | ∃ A : Finset ℕ, A.card = m ∧ IsAPCover (A : Set ℕ) N k } (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