On an irreducibility theorem of A. Schinzel associated with coverings of the integers

M. Filaseta, K. Ford, S. Konyagin

Research output: Contribution to journalArticle

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)xn + 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 languageEnglish (US)
Pages (from-to)633-643
Number of pages11
JournalIllinois Journal of Mathematics
Volume44
Issue number3
DOIs
StatePublished - Jan 1 2000
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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