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On two classes of simultaneous Pell equations with no solutions


Author: P. G. Walsh
Journal: Math. Comp. 68 (1999), 385-388
MSC (1991): Primary 11D09
DOI: https://doi.org/10.1090/S0025-5718-99-01048-0
MathSciNet review: 1622101
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Abstract: In this paper we describe two classes of simultaneous Pell equations of the form $x^2-dy^2=z^2-ey^2=1$ with no solutions in positive integers $x,y,z$. The proof is elementary and covers the case $(d,e)=(8,5)$, which was solved by E. Brown using very deep methods.


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Additional Information

P. G. Walsh
Affiliation: Department of Mathematics, University of Ottawa, 585 King Edward Street, Ottawa, Ontario, K1N-6N5 Canada
Email: gwalsh@mathstat.uottawa.ca

DOI: https://doi.org/10.1090/S0025-5718-99-01048-0
Received by editor(s): February 2, 1996
Additional Notes: Supported by an N.S.E.R.C. Posdoctoral Fellowship
Article copyright: © Copyright 1999 American Mathematical Society

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