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On the number of terms in the irreducible factors of a polynomial over ℚ

  • A. Choudhry (a1) and A. Schinzel (a2)
  • DOI: http://dx.doi.org/10.1017/S001708950000848X
  • Published online: 01 May 2009
Abstract

All polynomials considered in this paper belong to ℚ[x] and reducibility means reducibility over ℚ. It has been established by one of us [5] that every binomial in ℚ[x] has an irreducible factor which is either a binomial or a trinomial. He has further raised the question “Does there exist an absolute constant K such that every trinomial in ℚ[x] has a factor irreducible over ℚ which has at most K terms (i.e. K non-zero coefficients)?”

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2.H. L. Dorwart , Irreducibility of polynomials, Amer. Math. Monthly 42 (1935), 369381.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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