Theorems · Theorem · number theory
isPrimitiveRoot_of_mem_rootsOfUnity
∀ {M : Type u_1} [inst : CommMonoid M] {u : Mˣ} {n : ℕ} [NeZero n],
u ∈ rootsOfUnity n M → ∃ d, d ≠ 0 ∧ d ∣ n ∧ IsPrimitiveRoot u d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidNeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- LT.lt.ne'proof · cited by 1,417
- IsPrimitiveRootstatement · cited by 356
- orderOfproof · cited by 324
- rootsOfUnitystatement and proof · cited by 118
- NeZero.posproof · cited by 57
- orderOf_dvd_of_pow_eq_oneproof · cited by 24
- IsOfFinOrder.orderOf_posproof · cited by 17
- isPeriodicPt_mul_iff_pow_eq_oneproof · cited by 11
- IsPrimitiveRoot.orderOfproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.rootsOfUnityMapQuot_injectiveproof · cited by 2