The book I'm reading says that given a qth root of unity \[\zeta\], every polyonomial in \[\zeta\] can be expressed as
\[A_1\zeta^1 + A_2\zeta^2 + A_3\zeta^3 +A_4\zeta^4...A_{q1} + \zeta^{q1}\]
and the expression is unique because the cyclotomic polynomial of degree q1 of which \[\zeta\] is a zero is irreducible over the rational field so \[\zeta\] can't be a root of a polynomial of lower degree with integral coefficients.
I know the proof that cyclotomic polynomials are irreducible but I don't get why..... (don't even know what I'm unclear about).
I'm lost. I asked the question I asked orignally because I thought it might help me understand.
Last fiddled with by wildrabbitt on 20200303 at 21:39
