Theorems · Theorem · number theory

IsPrimitiveRoot.norm_eq_one_of_linearly_ordered

∀ {n : ℕ} {L : Type v} [inst : CommRing L] {ζ : L},
  IsPrimitiveRoot ζ n →
    ∀ {K : Type u_1} [inst_1 : Field K] [inst_2 : LinearOrder K] [IsStrictOrderedRing K] [inst_4 : Algebra K L],
      Odd n → (Algebra.norm K) ζ = 1

If K is linearly ordered, the norm of a primitive root is 1 if n is odd.

Defined in

Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots

Cited by

0 results in Mathlib

Foundations

Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldLinearOrderIsStrictOrderedRingAlgebra