Visibly irreducible polynomials over finite fields
Number Theory
2022-09-22 v1
Abstract
H. Lenstra has pointed out that a cubic polynomial of the form (x-a)(x-b)(x-c) + r(x-d)(x-e), where {a,b,c,d,e} is some permutation of {0,1,2,3,4}, is irreducible modulo 5 because every possible linear factor divides one summand but not the other. We classify polynomials over finite fields that admit an irreducibility proof with this structure.
Cite
@article{arxiv.1808.10440,
title = {Visibly irreducible polynomials over finite fields},
author = {Evan M. O'Dorney},
journal= {arXiv preprint arXiv:1808.10440},
year = {2022}
}
Comments
11 pages. To appear in the American Mathematical Monthly