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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Solving constrained Pell equations
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by Kiran S. Kedlaya PDF
Math. Comp. 67 (1998), 833-842 Request permission


Consider the system of Diophantine equations $x^2 - ay^2 = b$, $P(x,y) = z^{2}$, where $P$ is a given integer polynomial. Historically, such systems have been analyzed by using Baker’s method to produce an upper bound on the integer solutions. We present a general elementary approach, based on an idea of Cohn and the theory of the Pell equation, that solves many such systems. We apply the approach to the cases $P(x, y) = cy^2 + d$ and $P(x, y) = cx + d$, which arise when looking for integer points on an elliptic curve with a rational 2-torsion point.
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Additional Information
  • Kiran S. Kedlaya
  • Affiliation: Department of Mathematics Princeton University Princeton, New Jersey 08544
  • MR Author ID: 349028
  • ORCID: 0000-0001-8700-8758
  • Email:
  • Received by editor(s): January 11, 1995
  • Received by editor(s) in revised form: November 4, 1996
  • Additional Notes: This work was done during a summer internship at the Supercomputing Research Center (now Center for Computing Studies), Bowie, MD, in the summer of 1992.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 833-842
  • MSC (1991): Primary 11Y50; Secondary 11D09, 11D25
  • DOI:
  • MathSciNet review: 1443123