Talk:Cyclotomic identity
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Definition of the cyclotomic polynomials
[edit]This article contained the assertion that is a cyclotomic polynomial. I have changed the article to say that is the product of cyclotomic polynomials. Here's the explanation.
The n'th cyclotomic polynomial Φn(z) is defined by the equation
where 1 ≤ j ≤ n, only those j which are relatively prime to n are taken into the product, and ζ is a primitive n'th root of unity. For n > 2, Φn(z) does not have any real roots. But we can always express zn −1 as the product of cyclotomic polynomials:
where the product runs over the divisors of n. DavidCBryant 00:33, 18 May 2007 (UTC)