Holzer’s theorem in k[t]

José Luis Leal-Ruperto, David B. Leep

Research output: Contribution to journalArticlepeer-review

Abstract

Let a, b, c be nonzero polynomials in k[t] where k[t] is the ring of polynomials with coefficients in k. We prove that if ax2+by2+cz2=0 has a nonzero solution in k[t], then there exist x, y, z∈ k[ t] , not all zero, such that ax02+by02+cz02=0 and degx0≤12(degb+degc), degy0≤12(dega+degc), and degz0≤12(dega+degb). This is the polynomial analogue of Holzer’s theorem for ax2+by2+cz2=0 when a, b, c are integers.

Original languageEnglish
Pages (from-to)351-355
Number of pages5
JournalRamanujan Journal
Volume48
Issue number2
DOIs
StatePublished - Feb 15 2019

Keywords

  • Holzer’s theorem
  • Legendre equation
  • Rational polynomial ring

ASJC Scopus subject areas

  • Algebra and Number Theory

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