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Theorems · Theorem · number theory

IsPrimitiveRoot.isUnit

∀ {M : Type u_1} [inst : CommMonoid M] {k : ℕ} {ζ : M}, IsPrimitiveRoot ζ k → k ≠ 0 → IsUnit ζ
Defined in
Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots
Cited by
22 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
CommMonoid

Around this declaration

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

IsPrimitiveRoot.eq_pow_of_pow_eq_one · cited by 17IsPrimitiveRoot.eq_pow_of…IsPrimitiveRoot.pow_of_coprime · cited by 8IsPrimitiveRoot.pow_of_co…HasEnoughRootsOfUnity.natCard_rootsOfUnity · cited by 5HasEnoughRootsOfUnity.nat…IsPrimitiveRoot.isUnit_unit · cited by 4IsPrimitiveRoot.isUnit_un…IsPrimitiveRoot.pow_inj · cited by 4IsPrimitiveRoot.pow_injIsPrimitiveRoot.card_rootsOfUnity · cited by 3IsPrimitiveRoot.card_root…IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one · cited by 2Three.lambda_pow_four_dvd…modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_pow · cited by 2modularCyclotomicCharacte…IsCyclotomicExtension.Rat.Three.Units.mem · cited by 1Units.memMulChar.exists_mulChar_orderOf · cited by 1MulChar.exists_mulChar_or…IsCyclotomicExtension.Rat.Three.cube_sub_one_eq_mul · cited by 1Three.cube_sub_one_eq_mulIsCyclotomicExtension.Rat.Three.eta_sq · cited by 1Three.eta_sqIsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_one · cited by 1Three.eta_sq_add_eta_add_…IsCyclotomicExtension.Rat.Three.lambda_dvd_mul_sub_one_mul_sub_eta_add_one · cited by 1Three.lambda_dvd_mul_sub_…IsPrimitiveRoot.associated_pow_add_sub_sub_one · cited by 1IsPrimitiveRoot.associate…CommMonoid · cited by 2264CommMonoidIsUnit · cited by 1602IsUnitIsPrimitiveRoot · cited by 356IsPrimitiveRootpow_succ' · cited by 228pow_succ'IsPrimitiveRoot.pow_eq_one · cited by 48IsPrimitiveRoot.pow_eq_oneIsUnit.of_mul_eq_one · cited by 43IsUnit.of_mul_eq_oneIsPrimitiveRoot.isUnitCITED BYCITES

Cites6

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

Cited by22

Results whose statement or proof uses this declaration.