Theorems · Theorem · number theory

IsPrimitiveRoot.card_nthRoots

∀ {R : Type u_4} [inst : CommRing R] [inst_1 : IsDomain R] {n : ℕ} {ζ : R},
  IsPrimitiveRoot ζ n → ∀ (a : R), (Polynomial.nthRoots n a).card = if ∃ α, α ^ n = a then n else 0

Defined in

Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots

Cited by

2 results in Mathlib

Foundations

Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomain