On two classes of simultaneous Pell equations with no solutions

Walsh, P.

doi:10.1090/S0025-5718-99-01048-0

On two classes of simultaneous Pell equations with no solutions
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by P. G. Walsh PDF

Math. Comp. 68 (1999), 385-388 Request permission

Corrigendum: Math. Comp. 90 (2021), 2503-2505.

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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