Theorems · Theorem · number theory
IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_pow
∀ {k : ℕ} {K : Type u_1} [inst : Field K] {ζ : K} [inst_1 : CharZero K] [IsCyclotomicExtension {2 ^ (k + 2)} ℚ K]
(hζ : IsPrimitiveRoot ζ (2 ^ (k + 2))), (Algebra.norm ℤ) (hζ.toInteger - 1) = 2The norm, relative to ℤ, of ζ - 1 in a 2 ^ (k + 2)-th cyclotomic extension of ℚ is 2.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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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