Theorems · Theorem · number theory
IsPrimitiveRoot.zpowers_eq
∀ {R : Type u_4} [inst : CommRing R] [IsDomain R] {k : ℕ} [NeZero k] {ζ : Rˣ},
IsPrimitiveRoot ζ k → Subgroup.zpowers ζ = rootsOfUnity k R- Cited by
- 3 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- IsPrimitiveRootstatement and proof · cited by 356
- Subgroup.zpowersstatement · cited by 204
- AddEquiv.toEquivproof · cited by 174
- Nat.card_congrproof · cited by 133
- rootsOfUnitystatement · cited by 118
- IsPrimitiveRoot.pow_eq_oneproof · cited by 48
- Nat.card_zmodproof · cited by 13
- IsPrimitiveRoot.zmodEquivZPowersproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.eq_pow_of_mem_rootsOfUnityproof · cited by 3
- IsPrimitiveRoot.card_rootsOfUnity'proof · cited by 1
- IsPrimitiveRoot.map_rootsOfUnityproof · cited by 0