Polynomial Pell's equation

William A. Webb, Hisashi Yokota

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Consider the polynomial Pell's equation X2 - DY2 = 1, where D = A2 + 2C is a monic polynomial in Z[x] and deg C < deg A. Then for A, C ∈ script Q sign[x], deg C < 2, and B = A/C ∈ script Q sign[x], a necessary and sufficient condition for the polynomial Pell's equation to have a nontrivial solution in Z[x] is obtained.

Original languageEnglish
Pages (from-to)993-1006
Number of pages14
JournalProceedings of the American Mathematical Society
Volume131
Issue number4
DOIs
Publication statusPublished - 2003 Apr 1

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Keywords

  • Polynomial Pell's equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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