erdos_978.sub_one_density

Let `f ∈ ℤ[X]` be an irreducible polynomial. Suppose that the degree `k` of `f` is larger than `2`, and `f n` have no fixed `(k - 1)`-th power divisors other than `1`. Then the set of `n` such that `f n` is `(k - 1)`-th power free has positive density, and this is proved in [Ho67].

theorem erdos_978.sub_one_density {f : ℤ[X]} (hi : Irreducible f) (hd : f.natDegree > 2)
    (hp : ¬ ∃ p : ℕ, p.Prime ∧ ∀ n : ℕ, (p : ℤ) ^ (f.natDegree - 1) ∣ f.eval (n : ℤ)) :
    HasPosDensity {n : ℕ | Powerfree (f.natDegree - 1) (f.eval (n : ℤ))}

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