Theorems · Theorem · number theory
IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRoots
∀ {R : Type u_4} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : DecidableEq R] {n : ℕ},
Polynomial.nthRootsFinset n 1 = n.divisors.biUnion fun i => primitiveRoots i RnthRoots n as a Finset is equal to the union of primitiveRoots i R for i ∣ n.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDomainDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsDomainstatement and proof · cited by 2,196
- Finset.biUnionstatement and proof · cited by 217
- Nat.divisorsstatement and proof · cited by 137
- primitiveRootsstatement and proof · cited by 57
- Polynomial.nthRootsFinsetstatement · cited by 23
- Nat.divisors_zeroproof · cited by 12
- Polynomial.nthRootsFinset_zeroproof · cited by 4
- Polynomial.nthRootsFinset.congr_simpproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.prod_cyclotomic'_eq_X_pow_sub_oneproof · cited by 3
- nthRootsFinset_eq_of_primeproof · cited by 1