Source labels openChecked July 26, 2026

Ben Green's Open Problem 72

Green's Open Problem 72 / No-three-in-line problem*: The no-k-in-line conjecture holds for $k = 3$ .

Combinatorics AMS 5 AMS 52

Mathematical statement

Green's Open Problem 72 / No-three-in-line problem*: The no-k-in-line conjecture holds for $k = 3$ .

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_72

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_72 {N : ℕ} (hN : 3 ≤ N) : NoKInLineFor 3 N := 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 72background Wikipediabackground