Polynomial Pell's equation

William A. Webb; Hisashi Yokota

doi:10.1090/S0002-9939-02-06934-4

Polynomial Pell's equation

William A. Webb, Hisashi Yokota

Functional Control Systems

Research output: Contribution to journal › Article › peer-review

7 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 language	English
Pages (from-to)	993-1006
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-02-06934-4
Publication status	Published - 2003 Apr

Keywords

Polynomial Pell's equation

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-02-06934-4

Cite this

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AB - 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.

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Polynomial Pell's equation

Abstract

Keywords

ASJC Scopus subject areas

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