Source labels openChecked July 26, 2026

Erdős Problem 943

Let $A$ be the set of powerful numbers. Is is true that $1_A\ast 1_A(n)=n^{o(1)}$ for every $n$ ?

Number theory AMS 11

Mathematical statement

Let $A$ be the set of powerful numbers. Is is true that $1_A\ast 1_A(n)=n^{o(1)}$ for every $n$ ?

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_943

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_943 : answer(sorry) ↔    ∃ (o : ℕ → ℝ), o =o[atTop] (1 : ℕ → ℝ) ∧ ∀ᶠ n in atTop, (sumRep Powerful n) ≤ (n : ℝ)^(o 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 erdosproblems.com/943background