From: utzoo!decvax!ucbvax!G:shallit Newsgroups: net.math Title: Re: Questions about pizza answer Article-I.D.: populi.215 Posted: Wed Jun 23 10:37:06 1982 Received: Sun Jun 27 04:42:14 1982 [1] You hit the nail on the head. You CAN'T construct the 9-th roots, since there is no way to get them from cube roots. The only roots you can construct are products of a power of 2 and a set of Fermat primes. That set includes at most 1 of each prime. In particular, you can't construct the roots corresponding to powers of Fermat primes. [2] With respect to actually finding the roots of the polynomials in question, this can be done. The procedure is not terrible easy to describe, but I can give a reference: Jacobson's Basic Algebra I, pp. 215-218. I must admit this is rough going. But really one needs to be conversant with Galois theory to REALLY understand what is going on here. Herstein's Topics in Algebra is a good intro to Galois theory. /Jeff Shallit, Department of Mathematics, University of California, Berkeley