Theorems · Theorem · number theory
mem_primitiveRoots
∀ {R : Type u_4} {k : ℕ} [inst : CommRing R] [inst_1 : IsDomain R] {ζ : R},
0 < k → (ζ ∈ primitiveRoots k R ↔ IsPrimitiveRoot ζ k)- Cited by
- 18 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 13,712
- IsDomainstatement and proof · cited by 2,196
- IsPrimitiveRootstatement and proof · cited by 356
- Finset.mem_filterproof · cited by 185
- primitiveRootsstatement · cited by 57
- IsPrimitiveRoot.pow_eq_oneproof · cited by 48
- Multiset.mem_toFinsetproof · cited by 39
- Polynomial.mem_nthRootsproof · cited by 9
Cited by18
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.isRoot_cyclotomicproof · cited by 4
- IsPrimitiveRoot.card_primitiveRootsproof · cited by 4
- isPrimitiveRoot_of_mem_primitiveRootsproof · cited by 3
- Polynomial.sub_one_pow_totient_lt_cyclotomic_evalproof · cited by 2
- IsPrimitiveRoot.primitiveRoots_oneproof · cited by 2
- mem_nthRootsFinset_iff_of_primeproof · cited by 1
- Polynomial.cyclotomic_eval_lt_add_one_pow_totientproof · cited by 1
- autEquivRootsOfUnity_smulproof · cited by 1
- autEquivZmod_symm_apply_intCastproof · cited by 1
- isSplittingField_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- exists_root_adjoin_eq_top_of_isCyclicproof · cited by 1
- IsPrimitiveRoot.is_roots_of_minpolyproof · cited by 1