Source labels openChecked July 26, 2026

Ben Green's Open Problem 31: Zmod P

It is not known whether or not there exists a Sidon subset of $\mathbb{Z}/p\mathbb{Z}$ of size $(1 + o(1))\sqrt{p}$ , for all $p$ [Gr24].

Combinatorics AMS 5 AMS 11

Mathematical statement

It is not known whether or not there exists a Sidon subset of $\mathbb{Z}/p\mathbb{Z}$ of size $(1 + o(1))\sqrt{p}$ , for all $p$ [Gr24].

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_31.variants.zmod_p

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_31.variants.zmod_p : answer(sorry) ↔    ∃ S : (n : ℕ) → Finset (ZMod n),    ∃ o : ℕ → ℝ,      (o =o[atTop] fun _ : ℕ ↦ (1 : ℝ)) ∧      (∀ p, p.Prime → IsSidon (S p : Set (ZMod p))) ∧      (∀ p, p.Prime → ((S p).card : ℝ) = (1 + o p) * Real.sqrt (p : ℝ)) := 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 31background