Theorems · Theorem · number theory
IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two
∀ {K : Type u} [inst : Field K] {ζ : K} [inst_1 : CharZero K] [IsCyclotomicExtension {2} ℚ K]
(hζ : IsPrimitiveRoot ζ 2), (Algebra.norm ℤ) (hζ.toInteger - 1) = -2The norm, relative to ℤ, of ζ - 1 in a 2-th cyclotomic extension of ℚ is -2.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CharZerostatement and proof · cited by 932
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- NumberField.RingOfIntegersstatement · cited by 413
- IsPrimitiveRootstatement and proof · cited by 356
- IsCyclotomicExtensionstatement and proof · cited by 220
- Algebra.normstatement and proof · cited by 155
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.associated_norm_zeta_sub_oneproof · cited by 3
- IsPrimitiveRoot.prime_dvd_of_dvd_norm_sub_oneproof · cited by 1