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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Keywords: Pell's equations, polynomial diophantine equations
Article copyright: © Copyright 1976 American Mathematical Society