Theorems · Theorem · number theory
IsPrimitiveRoot.pow_eq_one_iff_dvd
∀ {M : Type u_1} [inst : CommMonoid M] {k : ℕ} {ζ : M}, IsPrimitiveRoot ζ k → ∀ (l : ℕ), ζ ^ l = 1 ↔ k ∣ l- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- one_powproof · cited by 521
- IsPrimitiveRootstatement and proof · cited by 356
- pow_mulproof · cited by 210
- IsPrimitiveRoot.pow_eq_oneproof · cited by 48
- IsPrimitiveRoot.dvd_of_pow_eq_oneproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_applyproof · cited by 1
- MulChar.exists_mulChar_orderOfproof · cited by 1
- IsPrimitiveRoot.adjoin_pair_eqproof · cited by 1
- IsPrimitiveRoot.zpow_eq_one_iff_dvdproof · cited by 1
- IsCyclic.exists_apply_ne_oneproof · cited by 1