2 research outputs found

    Visibly irreducible polynomials over finite fields

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    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

    Irreducible Cubics Modulo Five

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