Square-free smooth polynomials in residue classes and generators of irreducible polynomials

2022/01/17 by Bagshaw, Christian
#11T06 #11T24 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2201.06663

Abstract

Building upon the work of A. Booker and C. Pomerance (2017), we prove that for a prime power q ≥ 7, every residue class modulo an irreducible polynomial F ∈ \mathbbF_q[X] has a non-constant, square-free representative which has no irreducible factors of degree exceeding deg~F -1. We also give applications to generating sequences of irreducible polynomials.

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