Talk:Cyclotomic identity

Latest comment: 17 years ago by DavidCBryant in topic Definition of the cyclotomic polynomials

Definition of the cyclotomic polynomials

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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 ≤ jn, 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)Reply