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Theorems · Theorem · number theory

IsPrimitiveRoot.toInteger_isPrimitiveRoot

∀ {K : Type u} [inst : Field K] {ζ : K} {k : ℕ} [inst_1 : NeZero k] (hζ : IsPrimitiveRoot ζ k),
  IsPrimitiveRoot hζ.toInteger k
Defined in
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic
Cited by
15 results in Mathlib
Foundations
Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNeZero

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one · cited by 2Three.lambda_pow_four_dvd…IsCyclotomicExtension.Rat.associated_sub_one_of_isPrimitiveRoot · cited by 1Rat.associated_sub_one_of…IsCyclotomicExtension.Rat.associated_zeta_sub_one_pow_prime · cited by 1Rat.associated_zeta_sub_o…IsCyclotomicExtension.Rat.Three.Units.mem · cited by 1Units.memIsPrimitiveRoot.toInteger_cube_eq_one · cited by 1IsPrimitiveRoot.toInteger…IsCyclotomicExtension.Rat.Three.cube_sub_one_eq_mul · cited by 1Three.cube_sub_one_eq_mulIsCyclotomicExtension.Rat.Three.eta_sq · cited by 1Three.eta_sqIsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_one · cited by 1Three.eta_sq_add_eta_add_…IsCyclotomicExtension.Rat.Three.lambda_dvd_mul_sub_one_mul_sub_eta_add_one · cited by 1Three.lambda_dvd_mul_sub_…NumberField.Units.dvd_torsionOrder_of_isPrimitiveRoot · cited by 1Units.dvd_torsionOrder_of…IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow · cited by 1Rat.map_eq_span_zeta_sub_…IsCyclotomicExtension.Rat.mem_zpowers_galEquivZMod_of_mem_stabilizer · cited by 1Rat.mem_zpowers_galEquivZ…IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvd · cited by 1Rat.ramificationIdx_eq_of…IsCyclotomicExtension.Rat.Three.coe_eta · cited by 0Three.coe_etaIsCyclotomicExtension.Rat.Three.eq_one_or_neg_one_of_unit_of_congruent · cited by 0Three.eq_one_or_neg_one_o…Field · cited by 7404FieldNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersIsPrimitiveRoot · cited by 356IsPrimitiveRootIsPrimitiveRoot.toInteger · cited by 72IsPrimitiveRoot.toIntegerNumberField.RingOfIntegers.coe_injective · cited by 9RingOfIntegers.coe_inject…IsPrimitiveRoot.of_map_of_injective · cited by 2IsPrimitiveRoot.of_map_of…IsPrimitiveRoot.toInteger_isP…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.