Theorems · Theorem · number theory
IsPrimitiveRoot.pow_eq_one
∀ {M : Type u_1} [inst : CommMonoid M] {ζ : M} {k : ℕ}, IsPrimitiveRoot ζ k → ζ ^ k = 1- Cited by
- 48 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- IsPrimitiveRootstatement and proof · cited by 356
Cited by49
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.isUnitproof · cited by 22
- IsPrimitiveRoot.map_of_injectiveproof · cited by 19
- mem_primitiveRootsproof · cited by 18
- IsPrimitiveRoot.toRootsOfUnityproof · cited by 9
- IsPrimitiveRoot.uniqueproof · cited by 8
- IsPrimitiveRoot.powproof · cited by 8
- IsPrimitiveRoot.pow_of_coprimeproof · cited by 8
- IsPrimitiveRoot.norm'_eq_oneproof · cited by 5
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- IsPrimitiveRoot.pow_eq_one_iff_dvdproof · cited by 5
- IsPrimitiveRoot.eq_neg_one_of_two_rightproof · cited by 5
- IsPrimitiveRoot.isPrimitiveRoot_iffproof · cited by 3