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Irreducibility criteria for compositions of polynomials with integer coefficients

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Abstract

We provide irreducibility criteria for some classes of compositions of polynomials with integer coefficients of the form \(F\circ G\), with F being a quadratic irreducible polynomial and G a polynomial of arbitrary degree.

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Acknowledgments

The authors are grateful to an anonymous referee for suggestions that improved the presentation of the paper.

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Authors and Affiliations

  1. Research Unit 5, Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest, 014700, Romania

    Nicolae Ciprian Bonciocat & Mihai Cipu

  2. Université de Strasbourg, Mathématiques, 7, rue René Descartes, 67084, Strasbourg Cedex, France

    Yann Bugeaud & Maurice Mignotte

Authors
  1. Nicolae Ciprian Bonciocat
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  2. Yann Bugeaud
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  3. Mihai Cipu
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  4. Maurice Mignotte
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Corresponding author

Correspondence to Nicolae Ciprian Bonciocat.

Additional information

Communicated by J. Schoißengeier.

To Professor Kalman Győry, on the occasion of his $$75\mathrm{th}$$ 75 th birthday.

This work was supported by a 2015 LEA Math-Mode project.

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Bonciocat, N.C., Bugeaud, Y., Cipu, M. et al. Irreducibility criteria for compositions of polynomials with integer coefficients. Monatsh Math 182, 499–512 (2017). https://doi.org/10.1007/s00605-016-0890-4

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  • DOI: https://doi.org/10.1007/s00605-016-0890-4

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