Theorems · Theorem · number theory
IsPrimitiveRoot.zpow_eq_one_iff_dvd
∀ {G : Type u_3} [inst : DivisionCommMonoid G] {k : ℕ} {ζ : G}, IsPrimitiveRoot ζ k → ∀ (l : ℤ), ζ ^ l = 1 ↔ ↑k ∣ l- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- IsPrimitiveRootstatement and proof · cited by 356
- inv_oneproof · cited by 301
- zpow_natCastproof · cited by 271
- zpow_negproof · cited by 198
- DivisionCommMonoidstatement and proof · cited by 80
- inv_injproof · cited by 25
- dvd_negproof · cited by 19
- IsPrimitiveRoot.pow_eq_one_iff_dvdproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_powproof · cited by 2