On the Diophantine System $x^2 - Dy^2 = 1-D$ and $x=2z^2-1$
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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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2019 ◽
Vol 15
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pp. 1069-1074
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1998 ◽
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pp. 581-586
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Vol 11
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pp. 1850056
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2018 ◽
Vol 2018
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pp. 1-13
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pp. 88-100
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2014 ◽
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pp. 1921-1927
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2015 ◽
Vol 713-715
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pp. 1483-1486
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