Source labels openChecked July 26, 2026

Green's Open Problem 25

For which values of $k$ is the following true: whenever we partition $[N] = A_1 \cup \dots \cup A_k$ , $\left|\bigcup^k_{i=1} (A_i \hat{+} A_i)\right| \geq \frac{1}{10} N$ ?

Combinatorics AMS 5 AMS 11

Mathematical statement

For which values of $k$ is the following true: whenever we partition $[N] = A_1 \cup \dots \cup A_k$ , $\left|\bigcup^k_{i=1} (A_i \hat{+} A_i)\right| \geq \frac{1}{10} N$ ?

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_25

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_25 : {k : ℕ → ℕ | ∀ᶠ N in atTop, Property25 (k N) 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