Theorems · Theorem · number theory
IsPrimitiveRoot.card_rootsOfUnity
∀ {R : Type u_4} [inst : CommRing R] [IsDomain R] {ζ : R} {n : ℕ} [NeZero n],
IsPrimitiveRoot ζ n → Nat.card ↥(rootsOfUnity n R) = n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- Nat.cardstatement · cited by 844
- IsPrimitiveRootstatement and proof · cited by 356
- rootsOfUnitystatement · cited by 118
- IsPrimitiveRoot.isUnitproof · cited by 22
- IsPrimitiveRoot.coe_units_iffproof · cited by 11
- IsPrimitiveRoot.card_rootsOfUnity'proof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Complex.card_rootsOfUnityproof · cited by 1
- card_rootsOfUnity_eq_iff_exists_isPrimitiveRootproof · cited by 1
- IsPrimitiveRoot.autToPow_eq_modularCyclotomicCharacterstatement and proof · cited by 0