Source labels openChecked July 26, 2026

Erdős Problem 1145

Let $A=\{1\leq a_1 < a_2 < \cdots\}$ and $B=\{1\leq b_1 < b_2 < \cdots\}$ be sets of integers with $a_n/b_n\to 1$ .

Combinatorics AMS 5

Mathematical statement

Let $A=\{1\leq a_1 < a_2 < \cdots\}$ and $B=\{1\leq b_1 < b_2 < \cdots\}$ be sets of integers with $a_n/b_n\to 1$ .

If $A+B$ contains all sufficiently large positive integers then is it true that $\limsup 1_A\ast 1_B(n)=\infty$ ?

A conjecture of Erdős and Sárközy.

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_1145

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1145 : answer(sorry) ↔ Erdos1145Prop := 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/28background erdosproblems.com/1145background