Source labels openChecked July 26, 2026

Erdős Problem 156

Does there exist a maximal Sidon set $A\subset \{1,\ldots,N\}$ of size $O(N^{1/3})$ ?

Combinatorics AMS 5

Mathematical statement

Does there exist a maximal Sidon set $A\subset \{1,\ldots,N\}$ of size $O(N^{1/3})$ ?

A question of Erdős, Sárközy, and Sós [ESS94].

Statement source: Erdős 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

erdos_156

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_156 :    answer(sorry) ↔      (fun N ↦ (minMaximalSidonSet N : ℝ)) =O[atTop] (fun N ↦ (N : ℝ) ^ (1 / 3 : 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 erdosproblems.com/156background