Theorems · Theorem · number theory

IsPrimitiveRoot.zeta_sub_one_prime_of_two_pow

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

ζ - 1 is prime if ζ is a primitive 2 ^ (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 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCharZeroIsCyclotomicExtension