### Abstract

Let f(x) and g(x) be two relatively prime polynomials having integer coefficients with g(0) ≠ 0. The authors show that there is an N = N(f,g) such that if n ≥ N, then the non-reciprocal part of the polynomial f(x)x^{n} + g(x) is either irreducible or identically 1 or -1 with certain clear exceptions that arise from a theorem of Capelli. A version of this result is originally due to Andrzej Schinzel. The present paper gives a new approach that allows for an improved estimate on the value of N.

Original language | English (US) |
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Pages (from-to) | 633-643 |

Number of pages | 11 |

Journal | Illinois Journal of Mathematics |

Volume | 44 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2000 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Filaseta, M., Ford, K., & Konyagin, S. (2000). On an irreducibility theorem of A. Schinzel associated with coverings of the integers.

*Illinois Journal of Mathematics*,*44*(3), 633-643. https://doi.org/10.1215/ijm/1256060421