Factorization of a Formal Power Series with Constant Term Certain Power of a Prime

Abstract

This article explores formal power series with integer coefficients, specifically those of a particular form. The primary focus lies in the factorization and irreducibility criteria for these power series. An algorithm is presented for the factorization of power series with a constant term that is the cube of a prime, subject to specific conditions. Furthermore, we establish an irreducibility criterion applicable to power series with a constant term represented by the cube of a prime, as well as higher powers of a prime. The results not only contribute to the understanding of these specialized power series but also provide a practical algorithm for their factorization under certain constraints. The findings have broader implications for the study of power series with integer coefficients, offering insights into their structural properties and mathematical significance.