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Criteria for Simultaneous Solutions of X2 − DY2 = c and x2 − Dy2 = −c
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- Journal:
- Canadian Mathematical Bulletin / Volume 45 / Issue 3 / 01 September 2002
- Published online by Cambridge University Press:
- 20 November 2018, pp. 428-435
- Print publication:
- 01 September 2002
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- Article
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The purpose of this article is to provide criteria for the simultaneous solvability of the Diophantine equations
${{X}^{2}}-D{{Y}^{2}}\,=\,c$ and 
${{x}^{2}}-D{{y}^{2}}=-c$ when 
$c\,\in \,\mathbb{Z}$, and 
$D\,\in \,\mathbb{N}$ is not a perfect square. This continues work in [6]–[8].
