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Order from lowest to highest (1,2,3,6 instead of 6,3,2,1)
'''Cyclotomic''' (or "circle dividing") '''polynomials''' are the irreducible factors of <math>z^n - 1\!</math> when the polynomial coefficients are restricted to the field of [[rational number]]s. For example
'''Cyclotomic''' (or "circle dividing") '''polynomials''' are the irreducible factors of <math>z^n - 1\!</math> when the polynomial coefficients are restricted to the field of [[rational number]]s. For example
:<math> z^6-1 = (z^2-z+1) (z^2+z+1) (z+1) (z-1) </math>.
:<math> z^6-1 = (z-1) (z+1) (z^2+z+1) (z^2-z+1) </math>.
The cyclotomic polynomials are often written as <math>\Phi_n(z)</math>. The polynomial <math>z^n - 1\!</math> has exactly as many of these factors as there are integer divisors of n:
The cyclotomic polynomials are often written as <math>\Phi_n(z)</math>. The polynomial <math>z^n - 1\!</math> has exactly as many of these factors as there are integer divisors of n:
:<math> z^6 - 1 = \Phi_6(z)\Phi_3(z)\Phi_2(z)\Phi_1(z) </math>.
:<math> z^6 - 1 = \Phi_1(z)\Phi_2(z)\Phi_3(z)\Phi_6(z) </math>.
==Finding cyclotomic polynomials==
==Finding cyclotomic polynomials==