Theorems · Theorem · number theory
IsPrimitiveRoot.pow_of_dvd
∀ {M : Type u_1} [inst : CommMonoid M] {k : ℕ} {ζ : M},
IsPrimitiveRoot ζ k → ∀ {p : ℕ}, p ≠ 0 → p ∣ k → IsPrimitiveRoot (ζ ^ p) (k / p)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 38 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- IsPrimitiveRootstatement and proof · cited by 356
- IsPrimitiveRoot.eq_orderOfproof · cited by 18
- IsPrimitiveRoot.orderOfproof · cited by 10
- orderOf_pow_of_dvdproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.norm_pow_sub_one_twoproof · cited by 3
- Polynomial.cyclotomic_expand_eq_cyclotomicproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- IsCyclotomicExtension.of_union_of_dvdproof · cited by 1