From: utzoo!decvax!harpo!floyd!rjs Newsgroups: net.math Title: Questions about pizza answer Article-I.D.: floyd.306 Posted: Wed Jun 23 09:30:54 1982 Received: Sun Jun 27 03:47:57 1982 The answer to the pizza question was instructive (and in fact showed that you cannot divide a circle into 7 equal parts with a straight edge and compass). However, it does not show how to accomplish divisions it claims are possible. My questions are: I can see how to construct the roots of x^pq - 1 = 0 from the roots of x^p - 1 = 0 and x^q - 1 = 0 if p and q are mutually prime (all products of roots, one from each set are roots). But what if they are not mutually prime? Then there are roots (other than 1) in common and multiplying roots doesn't generate enough roots. I.e. how do you get the roots of x^9 - 1 = 0 from the roots of x^3 - 1 = 0? Once you try to get the roots for a Fermat prime > 3 you have the problem of finding roots of a polynomial of degree > 2. This is usually quite difficult, but all polynomials of interest are of the form 1 + x + x^2 + x^3 + ... + x^2^2^n. Is there an easy (or even known) method for finding these roots? Thanks. Robert Snyder, III (harpo!floyd!rjs)