IsPrimitiveRoot.card_primitiveRoots

∀ {R : Type u_4} [inst : CommRing R] [inst_1 : IsDomain R] {ζ : R} {k : ℕ},
  IsPrimitiveRoot ζ k → (primitiveRoots k R).card = k.totient

If an integral domain has a primitive k-th root of unity, then it has φ k of them.

Defined in: Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots
Cited by: 4 results in Mathlib
Foundations: Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.