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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polynomial Pell's equation


Authors: William A. Webb and Hisashi Yokota
Journal: Proc. Amer. Math. Soc. 131 (2003), 993-1006
MSC (1991): Primary 11D25, 11A55
Published electronically: November 6, 2002
MathSciNet review: 1948087
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Abstract: Consider the polynomial Pell's equation $X^2 -DY^2 = 1$, where $D = A^2 + 2C$is a monic polynomial in ${\mathcal Z}[x]$ and $\deg{C} < \deg{A}$. Then for $A, C \in {\mathcal Q}[x]$, $\deg{C} < 2$, and $B = A/C \in {\mathcal Q}[x]$, a necessary and sufficient condition for the polynomial Pell's equation to have a nontrivial solution in ${\mathcal Z}[x]$ is obtained.


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Additional Information

William A. Webb
Affiliation: Department of Mathematics, Washington State University, Pullman, Washington 99164
Email: webb@math.wsu.edu

Hisashi Yokota
Affiliation: Department of Mathematics, Hiroshima Institute of Technology, 2-1-1 Miyake Saeki-ku Hiroshima, Japan
Email: hyokota@cc.it-hiroshima.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06934-4
PII: S 0002-9939(02)06934-4
Keywords: Polynomial Pell's equation
Received by editor(s): April 3, 2001
Published electronically: November 6, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society