Divisibility criteria and coefficient formulas for cyclotomic polynomials
摘要
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomial and derive new formulas involving Ramanujan sums as an application of our results. Additionally, we provide new insights into the coefficients of cyclotomic polynomials and propose a recursive relation between the coefficients of two cyclotomic polynomials whose indexes differ by a prime factor.