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
Externally publishedYes

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Polynomials

Keywords

  • Polynomial Pell's equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Polynomial Pell's equation. / Webb, William A.; Yokota, Hisashi.

In: Proceedings of the American Mathematical Society, Vol. 131, No. 4, 04.2003, p. 993-1006.

Research output: Contribution to journalArticle

Webb, William A. ; Yokota, Hisashi. / Polynomial Pell's equation. In: Proceedings of the American Mathematical Society. 2003 ; Vol. 131, No. 4. pp. 993-1006.
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