Polynomial Pell's equation-II

W. A. Webb, H. Yokota

研究成果: Article

2 引用 (Scopus)

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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.

元の言語English
ページ(範囲)128-141
ページ数14
ジャーナルJournal of Number Theory
106
発行部数1
DOI
出版物ステータスPublished - 2004 5

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ASJC Scopus subject areas

  • Algebra and Number Theory

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