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arXiv · 2201.06663

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

Christian Bagshaw
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Abstract

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

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Christian Bagshaw. 2022-01-17. Square-free smooth polynomials in residue classes and generators of irreducible polynomials. https://arxiv.org/abs/2201.06663

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