SEMI-CYCLOTOMIC POLYNOMIALS

Abstract

If n is a positive integer, then the n th cyclotomic polynomial is defined as the unique monic polynomial having exactly the primitive n th roots of unity as its zeros. In this paper we start off by examining some of the properties of cyclotomic polynomials; specifically focusing on their irreducibility and how they relate to primes. After that we explore some applications of these polynomials, including proofs of Wedderburn's Theorem , and when a regular n-gon is constructible with a straightedge and compass.