Galois Theory and Cyclotomic Extensions

Abstract

Gauss was led to his discovery of constructible polygons from   over the set Q of rational numbers.  Inthis paper we examine that the factors of   and to show that how the Galois Theory can be used to determine that regular n-gons are constructible with a straightedge and compass. The irreducible factors of    are very important in number theory and in combinatorics.