Theorems · Theorem · number theory

nthRootsFinset_eq_of_prime

∀ {R : Type u_4} [inst : CommRing R] [inst_1 : IsDomain R] {p : ℕ} [inst_2 : DecidableEq R],
  Nat.Prime p → Polynomial.nthRootsFinset p 1 = primitiveRoots p R ∪ {1}

If p is prime, the p-th roots of unity in an integral domain are exactly the primitive p-th roots of unity together with 1.

Defined in

Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots

Cited by

1 results in Mathlib

Foundations

Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainDecidableEq