Source labels openChecked July 26, 2026

Erdős Problem 978: Ii

If $k>3$ (and $k \neq 2^l$ ), and for all primes $p$ there exists $n$ such that $p^{k-2}\nmid f(n)$ , then are there infinitely many $n$ for which $f(n)$ is $(k-2)$ -power-free?

Number theory AMS 11

Mathematical statement

If $k>3$ (and $k \neq 2^l$ ), and for all primes $p$ there exists $n$ such that $p^{k-2}\nmid f(n)$ , then are there infinitely many $n$ for which $f(n)$ is $(k-2)$ -power-free?

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_978.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_978.parts.ii : answer(sorry) ↔    ∀ {f : ℤ[X]}, Irreducible f → f.natDegree > 3 →    (¬ ∃ l : ℕ, f.natDegree = 2 ^ l) → 0 < f.leadingCoeff →    (∀ (p : ℕ), p.Prime → ∃ n : ℕ, ¬ (p : ℤ) ^ (f.natDegree - 2) ∣ f.eval (n : ℤ)) →    {n : ℕ | Powerfree (f.natDegree - 2) (f.eval (n : ℤ))}.Infinite := 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/978background