Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
algebraic number theory
constructibility of regular polygons factorization of x^n - 1 |
| gptkbp:coefficients |
integers
|
| gptkbp:definedIn |
minimal polynomials of primitive nth roots of unity over the rationals
|
| gptkbp:degree |
gptkb:Euler's_totient_function_φ(n)
|
| gptkbp:field |
gptkb:algebra
number theory |
| gptkbp:fifth_cyclotomic_polynomial |
Φ_5(x) = x^4 + x^3 + x^2 + x + 1
|
| gptkbp:first_cyclotomic_polynomial |
Φ_1(x) = x - 1
|
| gptkbp:fourth_cyclotomic_polynomial |
Φ_4(x) = x^2 + 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cyclotomic polynomials
|
| gptkbp:irreducible_over |
rational numbers
|
| gptkbp:namedFor |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:notation |
Φ_n(x)
|
| gptkbp:product_formula |
x^n - 1 = product over d|n of Φ_d(x)
|
| gptkbp:property |
symmetric polynomial
integer coefficients irreducible polynomial monic polynomial |
| gptkbp:relatedTo |
primitive roots
roots of unity cyclotomic fields |
| gptkbp:roots |
primitive nth roots of unity
|
| gptkbp:second_cyclotomic_polynomial |
Φ_2(x) = x + 1
|
| gptkbp:third_cyclotomic_polynomial |
Φ_3(x) = x^2 + x + 1
|
| gptkbp:used_in |
gptkb:Galois_theory
finite fields constructing regular polygons |
| gptkbp:bfsParent |
gptkb:Cyclotomic_fields
|
| gptkbp:bfsLayer |
8
|