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
Full-text PDF Free Access

Abstract | Similar Articles | Additional Information

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.


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10B15

Retrieve articles in all journals with MSC: 10B15


Additional Information

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