A polynomial given by Φ_n(x) = product_(k = 1)^n'(x - ζ_k), where ζ_k are the roots of unity in C given by ζ_k congruent e^(2π i k/n) and k runs over integers relatively prime to n. The prime may be dropped if the product is instead taken over primitive roots of unity, so that Φ_n(x) = product_(k = 1 primitive ζ_k)^n(x - ζ_k). The notation F_n(x) is also frequently encountered. Dickson et al. (1923) and Apostol give extensive bibliographies for cyclotomic polynomials.

Aurifeuillean factorization | Gauss's cyclotomic formula | Lucas's theorem | Möbius inversion formula | primitive root of unity | root of unity