### Abstract

We study integer coefficient polynomials of fixed degree and maximum height H
that are irreducible by the Dumas criterion. We call such polynomials Dumas polynomials. We derive upper bounds on the number of Dumas polynomials as H → ∞. We also show that, for a fixed degree, the density of Dumas polynomials in the set of all
irreducible integer coefficient polynomials is strictly less than 1.

Original language | English |
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Pages (from-to) | 1-7 |

Number of pages | 7 |

Journal | Journal of Integer Sequences |

Volume | 17 |

Issue number | 2 |

Publication status | Published - 2014 |

### Keywords

- Coprimality
- Dumas criterion
- Irreducible polynomial

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## Cite this

Heyman, R. (2014). On the number of polynomials of bounded height that satisfy the Dumas criterion.

*Journal of Integer Sequences*,*17*(2), 1-7.