Source labels openChecked July 26, 2026

Green's Open Problem 32

Let $p$ be a prime and let $A \subset \mathbb{Z}/p\mathbb{Z}$ be a set of size $\lfloor \sqrt{p} \rfloor$ . Is there a dilate of $A$ containing a gap of length $100\sqrt{p}$ ?

Combinatorics AMS 5 AMS 11

Mathematical statement

Let $p$ be a prime and let $A \subset \mathbb{Z}/p\mathbb{Z}$ be a set of size $\lfloor \sqrt{p} \rfloor$ . Is there a dilate of $A$ containing a gap of length $100\sqrt{p}$ ?

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_32

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_32 :    answer(sorry) ↔ HasLargeGapDilate (fun p ↦ Real.sqrt p) := 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