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Theorems · Theorem · number theory

IsPrimitiveRoot.eq_orderOf

∀ {M : Type u_1} [inst : CommMonoid M] {k : ℕ} {ζ : M}, IsPrimitiveRoot ζ k → k = orderOf ζ
Defined in
Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots
Cited by
18 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoid

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsPrimitiveRoot.map_of_injective · cited by 19IsPrimitiveRoot.map_of_in…HasEnoughRootsOfUnity.natCard_rootsOfUnity · cited by 5HasEnoughRootsOfUnity.nat…IsPrimitiveRoot.autToPow_spec · cited by 5IsPrimitiveRoot.autToPow_…IsPrimitiveRoot.pow_mul_pow_lcm · cited by 4IsPrimitiveRoot.pow_mul_p…IsPrimitiveRoot.pow_of_dvd · cited by 4IsPrimitiveRoot.pow_of_dvdIsPrimitiveRoot.associated_sub_one_pow_sub_one_of_coprime · cited by 3IsPrimitiveRoot.associate…NumberField.InfinitePlace.IsPrimitiveRoot.nrRealPlaces_eq_zero_of_two_lt · cited by 2IsPrimitiveRoot.nrRealPla…IsPrimitiveRoot.of_map_of_injective · cited by 2IsPrimitiveRoot.of_map_of…IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply · cited by 1Rat.galEquivZMod_restrict…Nat.exists_prime_gt_modEq_one · cited by 1Nat.exists_prime_gt_modEq…Polynomial.cyclotomic_injective · cited by 1Polynomial.cyclotomic_inj…IsCyclic.exists_apply_ne_one · cited by 1IsCyclic.exists_apply_ne_…IsPrimitiveRoot.card_rootsOfUnity' · cited by 1IsPrimitiveRoot.card_root…NumberField.Units.dvd_torsionOrder_of_isPrimitiveRoot · cited by 1Units.dvd_torsionOrder_of…IsCyclotomicExtension.Rat.mem_zpowers_galEquivZMod_of_mem_stabilizer · cited by 1Rat.mem_zpowers_galEquivZ…CommMonoid · cited by 2264CommMonoidIsPrimitiveRoot · cited by 356IsPrimitiveRootorderOf · cited by 324orderOfIsPrimitiveRoot.orderOf · cited by 10IsPrimitiveRoot.orderOfIsPrimitiveRoot.unique · cited by 8IsPrimitiveRoot.uniqueIsPrimitiveRoot.eq_orderOfCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.