Factorization of Polynomials over Z/(p n )

Abstract

In this paper, we deal with the problem of finding a factorization of a monic primary polynomial f ∈ Z/(pn)[x] into irreducible factors. This task has been completely solved when pn does not divide the discriminant of f, while there is not an efficient method of determining a factorization when this happens and finding an explicit factorization can be hard for polynomials of high degree. We discuss some techniques to speed up the computation, focusing on the case n=3.