2 results
Continued Fractions Associated with
$\text{S}{{\text{L}}_{3}}(\mathbf{Z})$ and Units in Complex Cubic Fields
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- Journal:
- Canadian Journal of Mathematics / Volume 54 / Issue 6 / 01 December 2002
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1305-1318
- Print publication:
- 01 December 2002
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- Article
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Continued fractions associated with
$\text{G}{{\text{L}}_{3}}\left( \mathbf{Z} \right)$ are introduced and applied to find fundamental units in a two-parameter family of complex cubic fields.
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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- You have access
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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].
