Source labels openChecked July 26, 2026

Ben Green's Open Problem 16

From [Yufei Zhao]: Is there a subset of $\{1, \ldots, N\}$ of size $N^{1/3 - o(1)}$ with no nontrivial solutions to $x + 2y + 3z = x' + 2y' + 3z'$ ?

Combinatorics AMS 5 AMS 11

Mathematical statement

From [Yufei Zhao]: Is there a subset of $\{1, \ldots, N\}$ of size $N^{1/3 - o(1)}$ with no nontrivial solutions to $x + 2y + 3z = x' + 2y' + 3z'$ ?

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

zhao_question

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem zhao_question :    ¬∃ h : ℕ → ℝ, Tendsto h atTop (𝓝 0) ∧ ∀ᶠ N in atTop, (g N : ℝ) ≥ (N : ℝ) ^ (1 / 3 - h 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 16background