Properties on Cyclotomic Polynomials and The Möbius function

Abstract

If n is a natural number, then the $ n^{th} $ cyclotomic polynomial denoted by ${\Phi_n(x)}$ and defined as the unique monic polynomial having exactly the primitive $ n^{th} $ roots of unity as its zeros. In this article we are going to derive properties related to cyclotomic polynomials using Mobious Inversion Formula