Theorems · Theorem · number theory
IsPrimitiveRoot.totient_le_degree_minpoly
∀ {n : ℕ} {K : Type u_1} [inst : CommRing K] {μ : K},
IsPrimitiveRoot μ n → ∀ [IsDomain K] [CharZero K], n.totient ≤ (minpoly ℤ μ).natDegreeThe degree of the minimal polynomial of μ is at least totient n.
- Defined in
- Mathlib.RingTheory.RootsOfUnity.Minpoly
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialproof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.natDegreestatement · cited by 1,105
- CharZerostatement and proof · cited by 932
- Polynomial.mapproof · cited by 806
- minpolystatement and proof · cited by 439
- IsPrimitiveRootstatement and proof · cited by 356
- Polynomial.rootsproof · cited by 264
- Int.castRingHomproof · cited by 254
- Finset.card_le_cardproof · cited by 118
- Nat.totientstatement · cited by 111
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_eq_minpolyproof · cited by 7