Theorems · Theorem · number theory
isRoot_of_unity_iff
∀ {n : ℕ},
0 < n →
∀ (R : Type u_2) [inst : CommRing R] [IsDomain R] {ζ : R},
ζ ^ n = 1 ↔ ∃ i ∈ n.divisors, (Polynomial.cyclotomic i R).IsRoot ζ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- Polynomialproof · cited by 5,681
- Multisetproof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.IsRootstatement and proof · cited by 152
- Nat.divisorsstatement and proof · cited by 137
- Polynomial.cyclotomicstatement and proof · cited by 130
- Polynomial.C_1proof · cited by 57
- Polynomial.mem_rootsproof · cited by 30
- Polynomial.X_pow_sub_C_ne_zeroproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_rootsproof · cited by 3
- IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_root_cyclotomicproof · cited by 2
- IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrderproof · cited by 1