Theorems · Theorem · number theory
IsPrimitiveRoot.zeta_sub_one_prime
∀ {p k : ℕ} {K : Type u} [inst : Field K] {ζ : K} [hp : Fact (Nat.Prime p)] [inst_1 : CharZero K]
[IsCyclotomicExtension {p ^ (k + 1)} ℚ K] (hζ : IsPrimitiveRoot ζ (p ^ (k + 1))), Prime (hζ.toInteger - 1)ζ - 1 is prime if ζ is a primitive p ^ (k + 1)-th root of unity.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- CharZerostatement and proof · cited by 932
- NumberField.RingOfIntegersstatement · cited by 413
- IsPrimitiveRootstatement and proof · cited by 356
- Primestatement · cited by 277
- IsCyclotomicExtensionstatement and proof · cited by 220
- IsPrimitiveRoot.toIntegerstatement · cited by 72
- IsPrimitiveRoot.zeta_sub_one_prime_of_ne_twoproof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_two_powproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.zeta_sub_one_prime'proof · cited by 1
- IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen_primeproof · cited by 0