Source labels openChecked July 26, 2026

Erdős Problem 938

Let $A=\{n_1 < n_2 < \cdots\}$ be the sequence of powerful numbers (if $p\mid n$ then $p^2\mid n$ ). Are there only finitely many three-term progressions of consecutive terms $n_k,n_{k+1},n_{k+2}$ ?

Number theory AMS 11

Mathematical statement

Let $A=\{n_1 < n_2 < \cdots\}$ be the sequence of powerful numbers (if $p\mid n$ then $p^2\mid n$ ). Are there only finitely many three-term progressions of consecutive terms $n_k,n_{k+1},n_{k+2}$ ?

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_938

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_938 : answer(sorry) ↔ {P : Finset ℕ | (P : Set ℕ).IsAPOfLength 3 ∧ ∃ k,    P = {nth Powerful k, nth Powerful (k + 1), nth Powerful (k + 2)}}.Finite := 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/938background