Theorems · Theorem · number theory
IsPrimitiveRoot.sub_one_dvd_sub
∀ {p : ℕ} {A : Type u_1} {ζ : A} [inst : CommRing A] [inst_1 : IsDomain A],
IsPrimitiveRoot ζ p →
Nat.Prime p →
∀ {η₁ : A}, η₁ ∈ Polynomial.nthRootsFinset p 1 → ∀ {η₂ : A}, η₂ ∈ Polynomial.nthRootsFinset p 1 → ζ - 1 ∣ η₁ - η₂If p is prime and ζ is a p-th primitive root of unity, then ζ - 1 divides η₁ - η₂
for all p-th roots of unity η₁ and η₂.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- IsDomainstatement and proof · cited by 2,196
- Nat.Primestatement and proof · cited by 2,059
- eq_or_neproof · cited by 1,117
- sub_selfproof · cited by 996
- IsPrimitiveRootstatement and proof · cited by 356
- Associated.dvdproof · cited by 38
- Polynomial.nthRootsFinsetstatement and proof · cited by 23
- IsPrimitiveRoot.nthRootsFinset_pairwise_associated_sub_one_sub_of_primeproof · cited by 2
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