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gptkbp:instanceOf
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Algebraic number field
Number field
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gptkbp:definedIn
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Field extension of the rationals generated by a primitive n-th root of unity
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gptkbp:degreeOverQ
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gptkb:Euler's_totient_function_φ(n)
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gptkbp:discriminant
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Known formula involving n and its prime divisors
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gptkbp:field
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gptkb:Algebraic_number_theory
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gptkbp:GaloisExtensionOf
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gptkb:Q
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gptkbp:GaloisGroup
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Isomorphic to (Z/nZ)×
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gptkbp:generation
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Primitive n-th root of unity
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https://www.w3.org/2000/01/rdf-schema#label
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Cyclotomic fields
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gptkbp:notation
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gptkb:Q(ζ_n)
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gptkbp:relatedTo
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gptkb:Dirichlet_characters
gptkb:Gauss_sums
gptkb:p-adic_L-functions
gptkb:Dirichlet_L-functions
gptkb:Kummer_extensions
gptkb:Kummer_theory
gptkb:Bernoulli_numbers
gptkb:Galois_cohomology
gptkb:Hilbert_class_field
gptkb:Iwasawa_theory
gptkb:Modular_forms
gptkb:Artin_reciprocity
gptkb:Stickelberger's_theorem
gptkb:Vandiver's_conjecture
gptkb:Cyclotomic_polynomials
gptkb:Eisenstein's_criterion
gptkb:Herbrand–Ribet_theorem
gptkb:Ramification_theory
gptkb:Roots_of_unity_group
gptkb:Stickelberger_element
gptkb:Teichmüller_character
L-functions
Roots of unity
Unit group
Complex multiplication
Galois module
Class group
Abelian extensions of Q
Class number problem
Prime decomposition in extensions
Torsion points
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gptkbp:ringOfIntegers
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Z[ζ_n]
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gptkbp:studiedBy
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gptkb:Leopold_Kronecker
gptkb:Richard_Dedekind
gptkb:Ernst_Kummer
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gptkbp:usedIn
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gptkb:Fermat's_Last_Theorem
gptkb:Kronecker–Weber_theorem
gptkb:Class_field_theory
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gptkbp:bfsParent
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gptkb:Cubic_reciprocity
gptkb:Global_class_field_theory
gptkb:Algebraic_Number_Fields
gptkb:Cyclotomic_extensions
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gptkbp:bfsLayer
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7
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