2 research outputs found
Visibly irreducible polynomials over finite fields
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.Comment: 11 pages. To appear in the American Mathematical Monthl