Cyclotomic polynomial
id:
cyclotomic-polynomial-176-17912744
title:
Cyclotomic polynomial
text:
In mathematics, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor of x n − 1 and is not a divisor of x k − 1 for any k < n. Its roots are all nth primitive roots of unity e 2 i π k n, where k runs over the positive integers less than n and coprime to n. In other words, the nth cyclotomic polynomial is equal to
- Φ n = ∏ gcd = 1 1 ≤ k ≤ n. It may also be defined as the monic polynomial with integer coeffic
brand slug:
wiki
category slug:
encyclopedia
description:
Irreducible polynomial whose roots are nth roots of unity
original url:
https://en.wikipedia.org/wiki/Cyclotomic_polynomial
date created:
2003-01-21T02:00:54Z
date modified:
2024-09-03T22:48:35Z
main entity:
{"identifier":"Q1051983","url":"https://www.wikidata.org/entity/Q1051983"}
image:
fields total:
13
integrity:
15