Theorems · Theorem · number theory
IsPrimitiveRoot.not_coprime_norm_of_mk_eq_one
∀ {K : Type u_1} [inst : Field K] {I : Ideal (NumberField.RingOfIntegers K)} [inst_1 : NumberField K],
Ideal.absNorm I ≠ 1 →
∀ {n : ℕ} {ζ : K} (hn : 2 ≤ n) (hζ : IsPrimitiveRoot ζ n),
(Ideal.Quotient.mk I) hζ.toInteger = 1 → ¬(Ideal.absNorm I).Coprime n- Cited by
- 1 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Factproof · cited by 2,726
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Nat.Primeproof · cited by 2,059
- map_oneproof · cited by 861
- MonoidWithZeroHomstatement · cited by 704
- NumberFieldstatement and proof · cited by 653
- Ideal.Quotient.mkstatement and proof · cited by 610
- NumberField.RingOfIntegersstatement and proof · cited by 413
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.rootsOfUnityMapQuot_injectiveproof · cited by 2