Polynomial Pell's equation-II

W. A. Webb, H. Yokota

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The polynomial Pell's equation is X2 - DY2 = 1, where D is a polynomial with integer coefficients and the solutions X, Y must be polynomials with integer coefficients. Let D = A2 + 2C be a polynomial in L[x], where deg C<deg A. Then for pB = pA/C ∈ L[x], p a prime, a necessary and sufficient condition for which the polynomial Pell's equation has a nontrivial solution is obtained. Furthermore, all solutions to the polynomial Pell's equation satisfying the above condition are determined.

Original languageEnglish
Pages (from-to)128-141
Number of pages14
JournalJournal of Number Theory
Volume106
Issue number1
DOIs
Publication statusPublished - 2004 May

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Keywords

  • Polynomial Pell's equation

ASJC Scopus subject areas

  • Algebra and Number Theory

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