Simultaneous Pell equations
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- by W. S. Anglin PDF
- Math. Comp. 65 (1996), 355-359 Request permission
Abstract:
Let $R$ and $S$ be positive integers with $R<S$. We shall call the simultaneous Diophantine equations \begin{align*} x^2-Ry^2&=1,\ z^2-Sy^2&=1 \end{align*} simultaneous Pell equations in $R$ and $S$. Each such pair has the trivial solution $(1,0,1)$ but some pairs have nontrivial solutions too. For example, if $R=11$ and $S=56$, then $(199, 60, 449)$ is a solution. Using theorems due to Baker, Davenport, and Waldschmidt, it is possible to show that the number of solutions is always finite, and it is possible to give a complete list of them. In this paper we report on the solutions when $R<S\le 200$.References
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Additional Information
- W. S. Anglin
- Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke West, Montreal, Quebec, Canada H3A 2K6
- Email: anglin@math.mcgill.ca
- Received by editor(s): June 8, 1994
- Received by editor(s) in revised form: October 11, 1994
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 355-359
- MSC (1991): Primary 11D09
- DOI: https://doi.org/10.1090/S0025-5718-96-00687-4
- MathSciNet review: 1325861