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gptkbp:instanceOf
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Polynomial
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gptkbp:coefficients
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Integers
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gptkbp:definedIn
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Integers
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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:Mathematics
gptkb:algebra
gptkb: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:hasProperty
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Integer coefficients
Irreducible polynomial
Monic polynomial
Symmetric polynomial
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gptkbp:hasSpecialCase
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Minimal polynomial
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https://www.w3.org/2000/01/rdf-schema#label
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Cyclotomic polynomial
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gptkbp:introduced
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gptkb:Gauss
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gptkbp:irreducible_over
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Rational numbers
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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 of Φ_d(x) over all d dividing n
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gptkbp:relatedTo
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Roots of unity
Cyclotomic field
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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:splits_over
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Cyclotomic field
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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
gptkb:Algebraic_number_theory
gptkb:Field_theory
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gptkbp:bfsParent
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gptkb:Cyclotomic_extensions
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gptkbp:bfsLayer
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7
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