Theorems · Theorem · number theory
IsPrimitiveRoot.coe_units_iff
∀ {M : Type u_1} [inst : CommMonoid M] {k : ℕ} {ζ : Mˣ}, IsPrimitiveRoot (↑ζ) k ↔ IsPrimitiveRoot ζ k- Cited by
- 11 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valstatement and proof · cited by 1,966
- IsPrimitiveRootstatement · cited by 356
Cited by11
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.eq_pow_of_pow_eq_oneproof · cited by 17
- IsPrimitiveRoot.pow_of_coprimeproof · cited by 8
- IsPrimitiveRoot.isUnit_unitproof · cited by 4
- IsPrimitiveRoot.card_rootsOfUnityproof · cited by 3
- Ideal.rootsOfUnityMapQuot_injectiveproof · cited by 2
- IsPrimitiveRoot.idealQuotient_mkproof · cited by 1
- ZMod.exists_monoidHom_apply_ne_oneproof · cited by 1
- card_rootsOfUnity_eq_iff_exists_isPrimitiveRootproof · cited by 1
- IsCyclotomicExtension.Rat.torsionOrder_eqproof · cited by 0
- MulEquiv.hasEnoughRootsOfUnityproof · cited by 0
- IsPrimitiveRoot.isUnit_unit'proof · cited by 0