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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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algebraic number theory
constructibility of regular polygons
factorization of x^n - 1
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gptkbp:coefficients
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integers
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gptkbp:definedIn
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minimal polynomials of primitive nth roots of unity over the rationals
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gptkbp:degree
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gptkb:Euler's_totient_function_φ(n)
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gptkbp:field
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gptkb:algebra
number theory
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gptkbp:fifth_cyclotomic_polynomial
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Φ_5(x) = x^4 + x^3 + x^2 + x + 1
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gptkbp:first_cyclotomic_polynomial
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Φ_1(x) = x - 1
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gptkbp:fourth_cyclotomic_polynomial
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Φ_4(x) = x^2 + 1
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gptkbp:irreducible_over
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rational numbers
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gptkbp:namedFor
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gptkb:Carl_Friedrich_Gauss
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gptkbp:notation
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Φ_n(x)
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gptkbp:product_formula
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x^n - 1 = product over d|n of Φ_d(x)
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gptkbp:property
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gptkb:symmetric_polynomial
integer coefficients
irreducible polynomial
monic polynomial
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gptkbp:relatedTo
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primitive roots
roots of unity
cyclotomic fields
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gptkbp:roots
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primitive nth roots of unity
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gptkbp:second_cyclotomic_polynomial
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Φ_2(x) = x + 1
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gptkbp:third_cyclotomic_polynomial
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Φ_3(x) = x^2 + x + 1
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gptkbp:used_in
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gptkb:Galois_theory
finite fields
constructing regular polygons
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gptkbp:bfsParent
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gptkb:Cyclotomic_fields
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gptkbp:bfsLayer
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8
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https://www.w3.org/2000/01/rdf-schema#label
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Cyclotomic polynomials
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