On the Diophantine System $x^2 - Dy^2 = 1-D$ and $x=2z^2-1$

Authors

  • Maohua Le

DOI:

https://doi.org/10.7146/math.scand.a-14455

Abstract

Let $D$ be a positive integer such that $D-1$ is an odd prime power. In this paper we give an elementary method to find all positive integer solutions $(x, y, z)$ of the system of equations $x^2-Dy^2=1-D$ and $x=2z^2-1$. As a consequence, we determine all solutions of the equations for $D=6$ and $8$.

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Published

2004-12-01

How to Cite

Le, M. (2004). On the Diophantine System $x^2 - Dy^2 = 1-D$ and $x=2z^2-1$. MATHEMATICA SCANDINAVICA, 95(2), 171–180. https://doi.org/10.7146/math.scand.a-14455

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Articles