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cyclotomic polynomial

irreducible polynomial of integer coefficients whose roots are nth roots of unity
Class type of: polynomial, irreducible polynomial Q1051983

Facts

5 properties
Subclass of
polynomial, irreducible polynomial
Defining formula
\Phi_n(x) =\prod_\stackrel{1\le k\le n}{\gcd(k,n)=1}\left(x-e^{2i\pi\frac{k}{n}}\right)
Has characteristic
degree of a polynomial[3]
Maintained by WikiProject
WikiProject Mathematics[6]
Studied by
algebraic number theory, Galois theory[4][5]
🏷️ Also known as
en cyclotomic polynomial ar متعددة حدود دويرانية cs cyklotomický polynom de Kreisteilungspolynom es polinomio ciclotómico es polinomio ciclotomico fr polynôme cyclotomique he הפולינום הציקלוטומי he פולינום ציקלוטומי hu körosztási polinom ja 円分多項式 ko 원분 다항식 ko 원분다항식 pl wielomian cyklotomiczny pt polinômio ciclotômico ro polinom ciclotomic ru круговой многочлен ru циклотомический многочлен sv cirkeldelningspolynom sv Cyklotomisk
🔖 Identifiers · 6
OpenAlex ID
C76253118
Freebase ID
/m/04_1kr2
MathWorld ID
CyclotomicPolynomial
Microsoft Academic ID (discontinued)
76253118
Rosetta Code page ID
Cyclotomic_polynomial
Treccani's Enciclopedia della Matematica ID
polinomio-ciclotomico

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🔗 Connections
Studied by 2
Galois theory, algebraic number theory
Subclass of 2
polynomial, irreducible polynomial
Has characteristic 1
degree of a polynomial
Maintained by WikiProject 1
WikiProject Mathematics
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Summary

cyclotomic polynomial is a type of polynomial[1] and irreducible polynomial[2].

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [1] ↑ . wikidata.org.
  2. [2] ↑ . wikidata.org.
  3. [3] ↑ . wikidata.org.
  4. [4] ↑ . wikidata.org.
  5. [5] ↑ . wikidata.org.
  6. [6] ↑ . wikidata.org.

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APA 4ort.xyz Knowledge Graph. (2026). cyclotomic polynomial. Retrieved November 6, 2026, from https://4ort.xyz/entity/cyclotomic-polynomial
MLA “cyclotomic polynomial.” 4ort.xyz Knowledge Graph, 4ort.xyz, 6 Nov. 2026, https://4ort.xyz/entity/cyclotomic-polynomial.
BibTeX @misc{4ortxyz_cyclotomic-polynomial_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{cyclotomic polynomial}}, year = {2026}, url = {https://4ort.xyz/entity/cyclotomic-polynomial}, note = {Accessed: 2026-11-06}}
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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 1d ago · Midleading · 2026-11-06 view diff on Wikidata ↗
    Defining formula → \Phi_n(x) =\prod_\stackrel{1\le k\le n}{\gcd(k,n)=1}\left(x-
    Wikipedia languages → ['ar', 'ca', 'cs', 'de', 'en', 'es', 'fr', 'he', 'hu', 'it', 'ja', 'ko', 'pl', '
    Claims rich → —
    "/* wbsetclaim-create:2||1 */ Defining formula: \Phi_n(x) =\prod_\stackrel{1\le k\le n}{\gcd(k,n)=1}\left(x-e^{2i\pi\frac{k}{n}}\right)"
  2. 8w ago · VGMaintenanceBot bot · 2026-09-08 view diff on Wikidata ↗
    Studied by → algebraic number theory, Galois theory
    Subclass of → polynomial, irreducible polynomial
    Has characteristic → degree of a polynomial
    Aliases → —
    + 2 other properties edited (see Wikidata diff for full list)
    "/* wbsetqualifier-add:1| */ MediaWiki page ID: 12711, Add qualifier to Rosetta Code page ID `Cyclotomic_polynomial`"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.