I have a series of questions regarding a cyclotomic polynomial of order p-1 where p is a prime; so there are p total terms in this polynomial because their is a constant term. I will post the questions 1 at a time, and as soon as I work my way through one i'll post the next one in this same thread.
Let's go !
First Question: If b is a root of this cyclotomic polynomial, show that b, b^2, .... b^p-1 are all distinct roots of this polynomial
The Attempt at a Solution
I'm at a bit of a loss as where to start, Perhaps it is of note that this polynomial is irreducible, and it is the pth cyclotomic polynomial (although this means it is of order p-1 where p is a prime). I suspect that these two factoids are going to play a role in the solution to understanding why any root will generate all the other roots. Anyone have some insight for me?