On the degrees of irreducible factors of polynomials over a finite field Original Research Article

Let Fq[X] denote the multiplicative semigroups of monic polynomials in one indeterminate X, over a finite field Fq. We determine for each fixed q, the asymptotic average number of distinct degrees of the irreducible factors of a polynomial of degree n in Fq[X]. The results are of relevance to various polynomial factorization algorithms.