ZMod 📖 | CompOp | 672 mathmath: ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_one, legendreSym.eq_neg_one_iff, ZMod.addOrderOf_coe, ZMod.intCast_eq_intCast_iff_dvd_sub, Submodule.toAddSubgroup_toZModSubmodule, ZMod.isUnit_iff_coprime, DirichletCharacter.changeLevel_injective, LucasLehmer.X.fst_natCast, DihedralGroup.r_one_zpow, ZMod.isCyclic_units_iff_of_odd, wittPolynomial_zmod_self, ZMod.injective_valMinAbs, EisensteinSeries.gammaSet_div_gcd_to_gammaSet10_bijection, ZMod.pow_card_sub_one, ZMod.χ₈'_int_eq_if_mod_eight, QuaternionGroup.a_one_pow_n, ZMod.unitsMap_surjective, Int.quotientSpanEquivZMod_comp_Quotient_mk, modularCyclotomicCharacter.id, Odd.intCast_zmod_two, QuaternionGroup.orderOf_a_one, ZMod.LFunction_modOne_eq, CongruenceSubgroup.Gamma_mem', ZMod.LFunction_stdAddChar_eq_expZeta, DirichletCharacter.Odd.eval_neg, ZMod.val_eq_one, DirichletCharacter.LSeries_eulerProduct_tprod, ZMod.rootsOfUnity_eq_top, AddSubgroupClass.coe_zmod_smul, WittVector.toZModPow_compat, tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries, WittVector.verschiebung_zmod, AddMonoidHom.toZModLinearMap_injective, ZMod.orderOf_one_add_mul_prime, LucasLehmer.X.ofNat_snd, QuaternionGroup.a_mul_xa, IsPrimitiveRoot.minpoly_dvd_pow_mod, Nat.sumByResidueClasses, PadicInt.zmod_congr_of_sub_mem_span, ZMod.units_pow_card_sub_one_eq_one, ZMod.intCast_cast_neg, ZMod.dft_even_iff, ZMod.invDFT_apply, ZMod.charpoly_pow_card, DirichletCharacter.LSeries_modOne_eq, IsCyclic.val_mulAutMulEquiv_apply, LucasLehmer.X.zero_fst, DirichletCharacter.changeLevel_def, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_three, ZMod.isCyclic_units_two_mul_iff_of_odd, DirichletCharacter.LSeriesSummable_of_one_lt_re, Int.quotientSpanNatEquivZMod_comp_Quotient_mk, ZMod.cast_one, cyclotomicCharacter.toZModPow, DirichletCharacter.conductor_le_conductor_mem_conductorSet, ZMod.ringEquivCongr_trans, LucasLehmer.X.neg_snd, ZMod.exists_sq_eq_neg_one_iff, ZMod.natCast_natAbs_valMinAbs, AddCommGroup.equiv_directSum_zmod_of_finite', ZMod.wilsons_lemma, DihedralGroup.r_pow, ZMod.dft_mul_const, ZMod.unitsMap_self, ZMod.intCast_cast_mul, DirichletCharacter.changeLevel_trans, ZMod.valMinAbs_neg_of_ne_half, DirichletCharacter.LSeries_twist_vonMangoldt_eq, ZMod.intCast_cast_add, autEquivZmod_symm_apply_natCast, ZMod.cast_intCast', CliffordAlgebra.toProd_comp_ofProd, quadraticChar_two, DirichletCharacter.LFunction_eq_LSeries, ZMod.val_unit', IsCyclic.unique_zpow_zmod, ZMod.val_natCast_of_lt, DirichletCharacter.norm_LSeries_product_ge_one, ZMod.stdAddChar_coe, ZMod.trace_pow_card, IsAddCyclic.unique_zsmul_zmod, ZMod.instMeasurableSingletonClass, ZMod.completedLFunction_zero, smulMemClass, CliffordAlgebra.toProd_ι_tmul_one, ZMod.natCast_eq_one_iff_odd, instIsReducedZModOfFactSquarefreeNat, ZMod.cast_add_eq_ite, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, ZMod.natCast_self, DirichletCharacter.LFunction_changeLevel, ZMod.isCyclic_units_one, DirichletCharacter.IsPrimitive.completedLFunction_one_sub, ZMod.not_isUnit_of_mem_primeFactors, ZMod.intCast_eq_iff, Nat.eq_sq_add_sq_iff_eq_sq_mul, ZMod.isCyclic_units_iff, ZMod.natCast_zmod_surjective, ZMod.minOrder_of_prime, ModN.basis_apply_eq_mkQ, ZMod.add_self_eq_zero_iff_eq_zero, ZMod.eq_zero_iff_even, modularCyclotomicCharacter.spec, Polynomial.natDegree_of_dvd_cyclotomic_of_irreducible, ZMod.LFunction_eq_LSeries, ZMod.χ₄_int_mod_four, DirichletCharacter.primitiveCharacter_one, AddAction.orbitZMultiplesEquiv_symm_apply', DirichletCharacter.norm_le_one, DirichletCharacter.mul_delta, Finset.sum_indicator_mod, AddAction.orbitZMultiplesEquiv_symm_apply, LucasLehmer.X.ofNat_fst, ZMod.AddAutEquivUnits_symm_apply, ZMod.ringHom_rightInverse, DirichletCharacter.eval_modulus_sub, Real.not_summable_indicator_one_div_natCast, CongruenceSubgroup.Gamma1_mem', ZMod.minOrder, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, ZMod.exists_sq_eq_two_iff, ZMod.val_pow_le, ZMod.val_injective, ZMod.inv_neg_one, ZMod.χ₈'_nat_eq_if_mod_eight, ZMod.cast_sub', ZMod.pow_totient, DirichletCharacter.unit_norm_eq_one, PadicInt.ext_of_toZModPow, DirichletCharacter.Odd.to_fun, ZMod.χ₈'_int_eq_χ₄_mul_χ₈, IsPrimitiveRoot.autToPow_eq_modularCyclotomicCharacter, DirichletCharacter.sum_characters_eq, CliffordAlgebra.map_mul_map_of_isOrtho_of_mem_evenOdd, ZMod.not_isCyclic_units_of_mul_coprime, CommGroup.equiv_prod_multiplicative_zmod_of_finite, Nat.card_units_zmod_lt_sub_one, ZMod.natCast_self', AddChar.zmod_add, FiniteField.instIsScalarTowerZModExtension, WittVector.fromPadicInt_comp_toPadicInt, ZMod.natCast_rightInverse, CliffordAlgebra.evenOdd.gradedMonoid, EisensteinSeries.gammaSetDivGcdSigmaEquiv_symm_eq, DirichletCharacter.toUnitHom_inj, IsPrimitiveRoot.coe_autToPow_apply, zmod_smul_mem, zmod_val_inv_nsmul_nsmul, AddSubgroup.toZModSubmodule_toAddSubgroup, DirichletCharacter.level_one', DirichletCharacter.LSeriesSummable_mul, ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_three, DirichletCharacter.conductor_one, LucasLehmer.sZMod_eq_sMod, ZMod.val_one'', GaloisField.finrank, ZMod.instIsSimpleAddGroup, ZMod.dft_comp_unitMul, ZMod.val_add, IsCyclotomicExtension.Rat.inertiaDegIn_of_not_dvd, ZMod.natCast_pow_eq_zero_of_le, DirichletCharacter.LSeries_changeLevel, DirichletCharacter.mulEquiv_units, LucasLehmer.X.ext_iff, ZMod.toAddCircle_inj, ZMod.instIsDomainOfNatNat, Odd.natCast_zmod_two, ZMod.inv_one, LucasLehmer.residue_eq_zero_iff_sMod_eq_zero, DihedralGroup.oddCommuteEquiv_symm_apply, EisensteinSeries.gammaSet_one_mem_iff, DirichletCharacter.changeLevel_one, ZMod.val_inv_mul, AddCommGroup.equiv_free_prod_directSum_zmod, ZMod.val_neg_of_ne_zero, ZMod.valMinAbs_natCast_of_le_half, ZMod.cast_pow', ZMod.val_mul, ZMod.valMinAbs_natCast_of_half_lt, ZMod.valMinAbs_zero, ZMod.val_cast_of_lt, IsPrimitiveRoot.autToPow_injective, CliffordAlgebra.range_ι_le_evenOdd_one, DirichletCharacter.Even.toUnitHom_eval_neg_one, ArithmeticFunction.pow_carmichael, ZMod.card_units, ZMod.card_units_eq_totient, DihedralGroup.oddCommuteEquiv_apply, ZMod.pow_card, ZMod.inv_coe_unit, IsCyclic.val_inv_mulAutMulEquiv_apply, DirichletCharacter.changeLevel_toUnitHom, ZMod.unitsMap_comp, ZMod.instSubsingletonUnits, ZMod.cast_injective_of_le, exists_prime_addEquiv_ZMod, ZMod.val_sub, DirichletCharacter.level_one, ZMod.instIsDomain, CliffordAlgebra.one_le_evenOdd_zero, DirichletCharacter.LSeries.mul_mu_eq_one, PadicInt.toZModPow_ofIntSeq_of_pow_dvd_sub, FiniteField.pow_finrank_eq_natCard, QuaternionGroup.a_mul_a, WittVector.frobeniusPoly_zmod, ZMod.natAbs_valMinAbs_eq_natAbs_valMinAbs, AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply, ZMod.val_one', ZMod.coe_int_inv_mul_eq_one, AddCommGroup.equiv_directSum_zmod_of_finite, autEquivZmod_symm_apply_intCast, FiniteField.finrank_zmod_extension, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow', ZMod.eq_neg_of_valMinAbs_eq_neg_valMinAbs, ZMod.ringEquivCongr_refl_apply, ZMod.χ₈'_eq_χ₄_mul_χ₈, Nat.range_mul_add, ZMod.coe_valMinAbs, AddChar.zmodChar_apply', ZMod.castHom_apply, ZMod.neg_val, eisSummand_of_gammaSet_eq_divIntMap, ZMod.algebraOfModule.proof, ZMod.isPrimitive_stdAddChar, legendreSym.at_two, ZMod.nonsquare_of_jacobiSym_eq_neg_one, TruncatedWittVector.commutes_symm', ZMod.intCast_abs_mod_two, Subfield.bot_eq_of_zMod_algebra, ZMod.forall, ZMod.isSquare_neg_one_iff, ZMod.val_one_eq_one_mod, QuaternionGroup.xa_mul_a, ZMod.lift_castAddHom, ZMod.mul_val_inv, ZMod.cast_natCast', ZMod.cast_one', WittVector.fromPadicInt_comp_toPadicInt_ext, ZMod.cast_add', ZMod.lift_comp_coe, ZMod.pow_card_sub_one_eq_one, ZMod.cast_zmod_eq_zero_iff_of_le, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, CoxeterSystem.lengthParity_comp_simple, ZMod.ringEquivCongr_symm, ZMod.ringEquivCongr_ringEquivCongr_apply, ZMod.invDFT_def', ZMod.natCast_eq_natCast_iff', QuaternionGroup.one_def, CliffordAlgebra.GradedAlgebra.ι_apply, ZMod.natCast_eq_iff, ZMod.AddAutEquivUnits_apply, ZMod.cast_mul', jacobiSym.at_neg_two, FiniteField.isSplittingField_of_nat_card_eq, legendreSym.eq_one_iff, ZMod.subsingleton_iff, IsPrimitiveRoot.minpoly_dvd_mod_p, ZMod.natCast_comp_val, ZMod.natCast_eq_zero_iff, gaussSum_mulShift_of_isPrimitive, ZMod.intCast_comp_cast, ZMod.completedLFunction_eq, ZMod.χ₈_int_mod_eight, TruncatedWittVector.charP_zmod, DihedralGroup.orderOf_r_one, instSubsingletonSubfieldZMod, FiniteField.two_pow_card, Int.quotientSpanEquivZMod_comp_castRingHom, ZMod.toAddCircle_natCast, quadraticChar_neg_two, ZMod.sq_add_sq, ZMod.euler_criterion_units, ZMod.instDiscreteTopology, ZMod.dft_apply, ZMod.castHom_self, ZMod.cast_cast_zmod_of_le, bijective_rootsOfUnityAddChar, IsCyclotomicExtension.Rat.inertiaDeg_eq, ZMod.valMinAbs_eq_zero, ZMod.natAbs_valMinAbs_neg, IsCyclotomicExtension.Rat.galEquivZMod_apply_of_pow_eq, DirichletCharacter.isPrimitive_one_level_one, IsPrimitiveRoot.separable_minpoly_mod, ZMod.val_zero, DihedralGroup.r_zpow, FiniteField.splits_X_pow_nat_card_sub_X, ZMod.eq_zero_iff_gcd_ne_one, ZMod.intCast_cast_sub, ZMod.isQuadratic_χ₈', LucasLehmer.X.add_snd, ZMod.invDFT_apply', AddSubgroup.toZModSubmodule_symm, LucasLehmer.sZMod_eq_s, IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_not_dvd, CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, ZMod.isQuadratic_χ₈, DirichletCharacter.isPrimitive_one_level_zero, DirichletCharacter.modOne_eq_one, DirichletCharacter.convolution_twist_vonMangoldt, PadicInt.toZMod_eq_residueField_comp_residue, EisensteinSeries.vecMul_SL2_mem_gammaSet, PadicInt.zmod_cast_comp_toZModPow, ZMod.nontrivial', LucasLehmer.X.one_fst, ZMod.val_neg_one, Subgroup.quotientEquivSigmaZMod_apply, surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar, ZMod.χ₄_nat_one_mod_four, ZMod.val_coe_unit_coprime, pow_zmod_val_inv_pow, jacobiSym.neg, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow, DihedralGroup.r_mul_r, ZMod.isCyclic_units_of_prime_pow, modularCyclotomicCharacter.unique, ZMod.ringHom_map_cast, ZMod.exists, not_summable_indicator_mod_of_antitone_of_neg, ZMod.dft_comp_neg, AddChar.zmodChar_apply, ZMod.ringHom_surjective, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, ZMod.cast_id', LucasLehmer.X.mul_fst, ZMod.val_neg', ZMod.gauss_lemma, ZMod.lift_comp_castAddHom, ZMod.exponent, ZMod.orderOf_one_add_four_mul, ZMod.intCast_eq_intCast_iff', MulAction.orbitZPowersEquiv_symm_apply, ZMod.intCast_zmod_eq_zero_iff_dvd, DirichletCharacter.LSeriesSummable_iff, ZMod.cast_sub, Nat.prime_iff_fac_equiv_neg_one, CommGroup.equiv_free_prod_prod_multiplicative_zmod, PadicInt.toZModPow_eq_iff_ext, ZMod.cast_natCast, ZMod.cast_neg_one, ZMod.χ₈_nat_mod_eight, ZMod.instSubsingletonAlgebra, MvPolynomial.frobenius_zmod, ZMod.coe_int_isUnit_iff_isCoprime, DihedralGroup.sr_mul_sr, AddSubgroup.coe_toZModSubmodule, ZMod.natCast_zmod_val, QuaternionGroup.a_one_pow, DirichletCharacter.IsPrimitive.fourierTransform_eq_inv_mul_gaussSum, ZMod.cast_zero, ZMod.isUnit_prime_iff_not_dvd, ZMod.intCast_eq_zero_iff_even, DirichletCharacter.changeLevel_factorsThrough, LucasLehmer.X.snd_intCast, FiniteField.isSplittingField_of_card_eq, Polynomial.dickson_one_one_zmod_p, ZMod.coe_int_mul_val_inv, ZMod.χ₄_int_three_mod_four, DirichletCharacter.absicssaOfAbsConv_eq_one, ZMod.dft_dft, ZMod.neg_eq_self_iff, ZMod.intCast_eq_intCast_iff, ZMod.cast_intCast, ZMod.ringEquivCongr_refl, legendreSym.eq_zero_iff, DirichletCharacter.eq_one_iff_conductor_eq_one, ZMod.χ₄_nat_three_mod_four, DirichletCharacter.sum_characters_eq_zero, ZMod.intCast_rightInverse, ZMod.lift_coe, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_coprime, QuaternionGroup.xa_mul_xa, DirichletCharacter.mul_convolution_distrib, ZMod.intCast_eq_one_iff_odd, PadicInt.ker_toZModPow, ZMod.χ₄_apply, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, CoxeterSystem.lengthParity_simple, ZMod.castHom_comp, DirichletCharacter.norm_LFunction_product_ge_one, CliffordAlgebra.prodEquiv_symm_apply, ZMod.natCast_eq_zero_iff_even, ZMod.charP, ZMod.val_add_val_of_le, ZMod.instSubsingletonModule, ZMod.orderOf_one_add_prime, ZMod.χ₄_int_one_mod_four, LucasLehmer.X.add_fst, Nat.prime_iff_card_units, IsPrimitiveRoot.squarefree_minpoly_mod, CliffordAlgebra.even_toSubmodule, ZMod.unitsMap_val, ZMod.nontrivial_iff, ZMod.addOrderOf_coe', ZMod.isCyclic_units_four, ZMod.LSeriesSummable_of_one_lt_re, DirichletCharacter.LSeries_eulerProduct_hasProd, MulAction.zpowersQuotientStabilizerEquiv_symm_apply, CliffordAlgebra.prodEquiv_apply, ZMod.χ₄_eq_neg_one_pow, FiniteField.splits_X_pow_card_sub_X, ZMod.cast_descFactorial, ZMod.intCast_mod, ZMod.toAddCircle_intCast, MulAction.orbitZPowersEquiv_symm_apply', tsum_dirichletSummand, ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_id, CongruenceSubgroup.Gamma1_mem, jacobiSym.at_two, ZMod.map_smul, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow', ZMod.toAddCircle_apply, FiniteField.pow_finrank_eq_card, ZMod.ker_intCastRingHom, ZMod.val_intCast, ZMod.natCast_smul_units, DirichletCharacter.LSeries_eulerProduct_exp_log, legendreSym.eq_one_iff', IsCyclotomicExtension.Rat.inertiaDegIn_eq, FiniteField.nonempty_algHom_extension, ZMod.val_natCast, ZMod.ker_intCastAddHom, legendreSym.eq_pow, instFiniteZModUnits, ZMod.orderOf_dvd_card_sub_one, TruncatedWittVector.card_zmod, LucasLehmer.X.mul_snd, ZMod.nontrivial, WittVector.toPadicInt_comp_fromPadicInt_ext, ZMod.orderOf_one_add_mul_prime_pow, legendreSym.at_neg_one, ZMod.isUnit_prime_of_not_dvd, CliffordAlgebra.ofProd_comp_toProd, ZMod.val_add_of_le, pow_pow_zmod_val_inv, ZMod.neg_eq_self_mod_two, quadraticChar_odd_prime, ZMod.isSquare_neg_one_iff', ZMod.frobenius_zmod, WittVector.toPadicInt_comp_fromPadicInt, CliffordAlgebra.evenOdd_mul_le, LucasLehmer.X.neg_fst, cyclotomicCharacter.toZModPow_toFun, ZMod.lift_injective, ZMod.mul_inv_eq_gcd, ZMod.castHom_bijective, ZMod.instSubsingletonSubfield, TruncatedWittVector.zmodEquivTrunc_apply, SL_reduction_mod_hom_val, DirichletCharacter.changeLevel_eq_one_iff, legendreSym.card_sqrts, ZMod.dft_const_mul, ZMod.val_mul_le, ZMod.gauss_lemma_aux, ZMod.infinite, PadicInt.zmod_congr_of_sub_mem_max_ideal, summable_indicator_mod_iff_summable, Even.intCast_zmod_two, LucasLehmer.X.fst_intCast, ZMod.cast_id, ZMod.toAddCircle_injective, ZMod.nonsquare_iff_jacobiSym_eq_neg_one, DirichletCharacter.FactorsThrough.existsUnique, Even.natCast_zmod_two, DihedralGroup.sr_mul_r, LucasLehmer.X.one_snd, IsCyclic.mulAutMulEquiv_symm_apply_symm_apply, CongruenceSubgroup.Gamma1_to_Gamma0_mem, DirichletCharacter.apply_eq_toArithmeticFunction_apply, modularCyclotomicCharacter.comp, ZMod.subsingleton_ringEquiv, ZMod.orderOf_lt, ArithmeticFunction.carmichael_eq_exponent', ZMod.not_isCyclic_units_eight, ZMod.expand_card, PadicInt.zmod_congr_of_sub_mem_span_aux, QuaternionGroup.xa_sq, ZMod.pow_card_pow, cyclotomicCharacter.spec, DirichletCharacter.not_LSeriesSummable_at_one, ZMod.one_eq_zero_iff, ZMod.val_one, CliffordAlgebra.toProd_one_tmul_ι, DirichletCharacter.changeLevel_self_toUnitHom, ZMod.val_mul', ZMod.instIsAddCyclic, ZMod.abs_valMinAbs_eq_abs_valMinAbs, ZMod.valMinAbs_natCast_eq_self, rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val, ZMod.natCast_mod, ZMod.val_two_eq_two_mod, ZMod.toCircle_intCast, ZMod.toCircle_natCast, ZMod.ringChar_zmod_n, ZMod.orderOf_five, ZMod.χ₈'_apply, ZMod.val_add_of_lt, ArithmeticFunction.carmichael_eq_exponent, ZMod.inv_zero, ZMod.coe_mul_inv_eq_one, lucas_primality_iff, Subgroup.transferFunction_apply, ZMod.invDFT_def, Polynomial.natDegree_of_mem_normalizedFactors_cyclotomic, legendreSym.eq_neg_one_iff', ZMod.injective_toCircle, legendreSym.at_neg_two, ZMod.χ₄_int_eq_if_mod_four, isReduced_zmod, ZMod.intCast_zmod_cast, AddChar.zmod_zero, IsPrimitiveRoot.autToPow_spec, ZMod.isCyclic_units_two, ZMod.isUnit_cast_of_dvd, ZMod.isSquare_of_jacobiSym_eq_one, TruncatedWittVector.commutes, ZMod.addOrderOf_one, ZMod.castHom_injective, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_isCoprime, ZMod.val_pow, IsCyclic.mulAutMulEquiv_symm_apply_apply, ZMod.coe_unitOfCoprime, DihedralGroup.r_one_pow_n, DirichletCharacter.factorsThrough_iff_ker_unitsMap, ZMod.natCast_eq_natCast_iff, ZMod.cast_pow, DihedralGroup.one_def, Nat.card_zmod, AddChar.zmodChar_primitive_of_primitive_root, modularCyclotomicCharacter'.spec', CoxeterSystem.lengthParity_eq_ofAdd_length, ZMod.cast_neg, ZMod.toCircle_apply, DirichletCharacter.delta_mul, ZMod.χ₄_nat_mod_four, ZMod.natAbs_mod_two, CliffordAlgebra.ι_mem_evenOdd_one, Subgroup.transferTransversal_apply'', PadicInt.ker_toZMod, ZMod.cast_sub_one, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat, ZMod.coe_int_mul_inv_eq_one, DirichletCharacter.isMultiplicative_toArithmeticFunction, DirichletCharacter.convolution_mul_moebius, ZMod.charZero, ZMod.isCyclic_units_two_pow_iff, ZMod.coe_unitOfIsCoprime, ZMod.toAddCircle_eq_zero, MvPolynomial.expand_zmod, IsCyclotomicExtension.Rat.inertiaDeg_of_not_dvd, ZMod.natAbs_valMinAbs_add_le, ZMod.LFunction_residue_one, quadraticChar_neg_one, AddMonoidHom.coe_toZModLinearMap, DihedralGroup.r_mul_sr, ZMod.isCyclic_units_zero, Quandle.dihedralAct.inv, Subgroup.quotientEquivSigmaZMod_symm_apply, instIsLocalHomZModRingHomOfIsLocalRingOfNontrivial, ZMod.subsingleton_ringHom, DirichletCharacter.Odd.toUnitHom_eval_neg_one, DirichletCharacter.factorsThrough_one_iff, DirichletCharacter.Even.to_fun, CliffordAlgebra.ofProd_ι_mk, ZMod.val_mul_iff_lt, CliffordAlgebra.GradedAlgebra.lift_ι_eq, AddSubgroup.mem_toZModSubmodule, QuaternionGroup.a_zero, ZMod.val_cast_eq_val_of_lt, ZMod.χ₈_nat_eq_if_mod_eight, DirichletCharacter.changeLevel_primitiveCharacter, DirichletCharacter.map_zero', TruncatedWittVector.commutes', ZMod.prod_Ico_one_prime, jacobiSym.at_neg_one, ZMod.coe_intCast, MvPolynomial.C_dvd_iff_zmod, ZMod.erdos_ginzburg_ziv, LucasLehmer.X.zero_snd, DirichletCharacter.modZero_eq_delta, ModN.instModuleFinite, DirichletCharacter.fourierTransform_eq_gaussSum_mulShift, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvd, ZMod.dft_eq_fourier, ZMod.dft_odd_iff, reverse_lucas_primality, ZMod.ringEquivCongr_val, ZMod.val_eq_zero, ZMod.isCyclic_units_prime, ZMod.neg_val', ZMod.fieldRange_castHom_eq_bot, EisensteinSeries.eisensteinSeries_slash_apply, AddChar.zmod_intCast, ZMod.instIsScalarTower, ZMod.ringEquivCongr_intCast, ZMod.natCast_toNat, ZMod.euler_criterion, ZMod.eq_unit_mul_divisor, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, DirichletCharacter.LSeries_eulerProduct, ZMod.val_mul_of_lt, ZMod.exists_sq_eq_neg_two_iff, CongruenceSubgroup.Gamma_mem, ZMod.injective_stdAddChar, DirichletCharacter.changeLevel_self, ZMod.val_cast_zmod_lt, AddChar.zmodAddEquiv_apply, ZMod.orderOf_units_dvd_card_sub_one, ZMod.isCyclic_units_four_mul_iff, ZMod.isQuadratic_χ₄, ZMod.dft_const_smul, CliffordAlgebra.evenOdd_isCompl, PadicInt.cast_toZModPow, ZMod.eisenstein_lemma_aux, ZMod.smul_mem, ZMod.dft_smul_const, EisensteinSeries.gammaSetDivGcdEquiv_eq, ZMod.completedLFunction_modOne_eq, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int, AddChar.zmod_injective, WittVector.zmodEquivTrunc_compat, DihedralGroup.r_one_pow, DihedralGroup.inv_r, ZMod.castHom_surjective, ZMod.dft_def, ZMod.smul_units_def, DirichletCharacter.conductor_one_dvd, DirichletCharacter.changeLevel_eq_cast_of_dvd, ZMod.coe_int_val_inv_mul, ZMod.χ₈_apply, ZMod.valMinAbs_spec, ZMod.intCast_surjective, modularCyclotomicCharacter'.unique', Polynomial.normalizedFactors_cyclotomic_card, ZMod.card, instIsAddKleinFourProdZModOfNatNat, PadicInt.val_toZMod_eq_zmodRepr, ZMod.rootsOfUnityAddChar_val, ZMod.toCircle_eq_circleExp, Int.quotientSpanNatEquivZMod_comp_castRingHom, ZMod.eq_zero_of_gcd_ne_one, PadicInt.toZMod_spec, ZMod.stdAddChar_apply, IsCyclotomicExtension.autEquivPow_symm_apply, EisensteinSeries.mem_gammaSet_one, cyclotomicCharacter.toFun_spec, ZMod.val_add_le, TruncatedWittVector.commutes_symm, DirichletCharacter.FactorsThrough.eq_changeLevel, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow, ZMod.cast_mul, IsDedekindDomain.selmerGroup.valuation_ker_eq, ZMod.χ₄_nat_eq_if_mod_four, IsCyclotomicExtension.autEquivPow_apply, DihedralGroup.r_zero, ZMod.dft_apply_zero, LucasLehmer.X.snd_natCast, ZMod.χ₈_int_eq_if_mod_eight, ZMod.instHasEnoughRootsOfUnityHSubNatOfNat, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, nsmul_zmod_val_inv_nsmul, ZMod.unitsMap_def, ZMod.cast_add, summable_indicator_mod_iff, WittVector.frobenius_zmodp, DirichletCharacter.Even.eval_neg, CongruenceSubgroup.Gamma0_mem, ZMod.pow_div_two_eq_neg_one_or_one, GaloisField.splits_zmod_X_pow_sub_X, ZMod.eq_one_iff_odd
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