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Further irreducibility criteria for polynomials with non-negative coefficients

Volume 175 / 2016

Morgan Cole, Scott Dunn, Michael Filaseta Acta Arithmetica 175 (2016), 137-181 MSC: Primary 11R09; Secondary 11C08, 12E05, 26C10. DOI: 10.4064/aa8376-5-2016 Published online: 15 September 2016

Abstract

Let $f(x)$ be a polynomial with non-negative integer coefficients. This paper produces sharp bounds $M_{1}(b)$ depending on an integer $b \in [3,20]$ such that if each coefficient of $f(x)$ is $\le M_{1}(b)$ and $f(b)$ is prime, then $f(x)$ is irreducible. A number of other related results are obtained.

Authors

  • Morgan ColeDepartment of Mathematics
    College of the Canyons
    26455 Rockwell Canyon Rd
    Santa Clarita, CA 91355, U.S.A.
    e-mail
  • Scott DunnDepartment of Mathematics
    University of South Carolina
    Columbia, SC 29208, U.S.A.
    e-mail
  • Michael FilasetaDepartment of Mathematics
    University of South Carolina
    Columbia, SC 29208, U.S.A.
    e-mail

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