Thread: algebraic numbers View Single Post
 2020-03-03, 21:36 #3 wildrabbitt   Jul 2014 3·149 Posts The book I'm reading says that given a qth root of unity $\zeta$, every polyonomial in $\zeta$ can be expressed as $A_1\zeta^1 + A_2\zeta^2 + A_3\zeta^3 +A_4\zeta^4...A_{q-1} + \zeta^{q-1}$ and the expression is unique because the cyclotomic polynomial of degree q-1 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 2020-03-03 at 21:39