Revision as of 15:47, 8 December 2008 by imported>Richard Pinch
In algebra, a cyclotomic polynomial is a polynomial whose roots are a set of primitive roots of unity. The n-th cyclotomic polynomial, denoted by Φn has integer cofficients.
For a positive integer n, let ζ be a primitive n-th root of unity: then
The degree of is given by the Euler totient function .
Since any n-th root of unity is a primitive d-th root of unity for some factor d of n, we have
By the Möbius inversion formula we have
where μ is the Möbius function.