Theorems · Theorem · number theory
IsPrimitiveRoot.self_sub_one_pow_dvd_order
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] {k n : ℕ},
k < n → ∀ {μ : R}, IsPrimitiveRoot μ n → ∃ z ∈ ℤ[μ], ↑n = z * (μ - 1) ^ kIf μ is a primitive nth root of unity in R and k < n, then n is divisible
by (μ-1)^k in ℤ[μ] ⊆ R.
- Defined in
- Mathlib.RingTheory.RootsOfUnity.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finset.sumproof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- Finset.prodproof · cited by 2,356
- Finset.cardproof · cited by 2,327
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- mul_assocproof · cited by 1,667
- Subalgebrastatement · cited by 1,353
- Finset.rangeproof · cited by 1,341
- Nat.cast_addproof · cited by 586
Cited by1
Results whose statement or proof uses this declaration.
- exists_jacobiSum_eq_neg_one_addproof · cited by 0