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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 equations


Author: Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 56 (1976), 89-92
MSC: Primary 10B15
MathSciNet review: 0401641
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Abstract: The polynomial Pell's equation is $ {P^2} - ({x^2} + d){Q^2} = 1$, where $ d$ is an integer and the solutions $ P,Q$ must be polynomials with integer coefficients. It is proved that this equation has nonconstant solutions if and only if $ d = \pm 1, \pm 2$, and in these cases all solutions are determined.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0401641-4
PII: S 0002-9939(1976)0401641-4
Keywords: Pell's equations, polynomial diophantine equations
Article copyright: © Copyright 1976 American Mathematical Society