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Theorems · Theorem · number theory

HasEnoughRootsOfUnity.exists_primitiveRoot

∀ (M : Type u_1) [inst : CommMonoid M] (n : ℕ) [HasEnoughRootsOfUnity M n], ∃ ζ, IsPrimitiveRoot ζ n
Defined in
Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity
Cited by
5 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CommMonoidHasEnoughRootsOfUnity
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Around this declaration

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

HasEnoughRootsOfUnity.natCard_rootsOfUnity · cited by 5HasEnoughRootsOfUnity.nat…HasEnoughRootsOfUnity.of_dvd · cited by 5HasEnoughRootsOfUnity.of_…modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_pow · cited by 2modularCyclotomicCharacte…CommGroup.exists_apply_ne_one_of_hasEnoughRootsOfUnity · cited by 2CommGroup.exists_apply_ne…cyclotomicCharacter.toFun_apply · cited by 1cyclotomicCharacter.toFun…CommMonoid · cited by 2264CommMonoidIsPrimitiveRoot · cited by 356IsPrimitiveRootHasEnoughRootsOfUnity · cited by 56HasEnoughRootsOfUnityHasEnoughRootsOfUnity.prim · cited by 2HasEnoughRootsOfUnity.primHasEnoughRootsOfUnity.exists_…CITED BYCITES

Cites4

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

Cited by5

Results whose statement or proof uses this declaration.