The Coefficients of Cyclotomic Polynomials

摘要

One of the most surprising properties of cyclotomic polynomials is that their coefficients are all 1, -1 or zero--at least that seems to be the case until one notices that the 105th cyclotomic polynomial has a coefficient of -2. This article serves as an introduction to these polynomials with a particular emphasis on their coefficients and proves that the coefficients of the first 104 cyclotomic polynomials are at most one in absolute value.