Source labels openChecked July 26, 2026

Erdős Problem 153

Let $A$ be a finite Sidon set and $A+A=\{s_1<\cdots<s_t\}$ . Is it true that $\frac{1}{t}\sum_{1\leq i<t}(s_{i+1}-s_i)^2 \to \infty$ as $\lvert A\rvert\to \infty$ ?

Combinatorics AMS 5

Mathematical statement

Let $A$ be a finite Sidon set and $A+A=\{s_1<\cdots<s_t\}$ . Is it true that $\frac{1}{t}\sum_{1\leq i<t}(s_{i+1}-s_i)^2 \to \infty$ as $\lvert A\rvert\to \infty$ ?

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_153

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_153 : answer(sorry) ↔ Tendsto f atTop atTop := 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/153background