Theorems · Theorem · number theory

IsPrimitiveRoot.zeta_sub_one_prime_of_ne_two

∀ {p k : ℕ} {K : Type u} [inst : Field K] {ζ : K} [hp : Fact (Nat.Prime p)] [inst_1 : CharZero K]
  [IsCyclotomicExtension {p ^ (k + 1)} ℚ K] (hζ : IsPrimitiveRoot ζ (p ^ (k + 1))), p ≠ 2 → Prime (hζ.toInteger - 1)

ζ - 1 is prime if p ≠ 2 and ζ is a primitive p ^ (k + 1)-th root of unity. See zeta_sub_one_prime for a general statement.

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Basic

Cited by

1 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFactCharZeroIsCyclotomicExtension