Polynomial Pell's equation |
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| Authors: | William A Webb Hisashi Yokota |
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| Institution: | Department of Mathematics, Washington State University, Pullman, Washington 99164 ; Department of Mathematics, Hiroshima Institute of Technology, 2-1-1 Miyake Saeki-ku Hiroshima, Japan |
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| Abstract: | Consider the polynomial Pell's equation  , where  is a monic polynomial in ![${\mathcal Z}x]$](http://www.ams.org/proc/2003-131-04/S0002-9939-02-06934-4/gif-abstract0/img3.gif) and  . Then for ![$A, C \in {\mathcal Q}x]$](http://www.ams.org/proc/2003-131-04/S0002-9939-02-06934-4/gif-abstract0/img5.gif) ,  , and ![$B = A/C \in {\mathcal Q}x]$](http://www.ams.org/proc/2003-131-04/S0002-9939-02-06934-4/gif-abstract0/img7.gif) , a necessary and sufficient condition for the polynomial Pell's equation to have a nontrivial solution in ![${\mathcal Z}x]$](http://www.ams.org/proc/2003-131-04/S0002-9939-02-06934-4/gif-abstract0/img8.gif) is obtained. |
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| Keywords: | Polynomial Pell's equation |
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