Visibly Irreducible Polynomials over Finite Fields
Evan M. O’Dorney · American Mathematical Monthly · 2020
Lenstra, in this Monthly, has pointed out that a cubic over F5=Z/5Z of the form (x−a)(x−b)(x−c)+λ(x−d)(x−e), where {a,b,c,d,e} is some permutation of {0,1,2,3,4}, is irreducible because every element of F5 is a root of one summand but not the other. We classify polynomials over finite fields that admit an irreducibility proof with this structure.