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Necessary and Sufficient Conditions for the Central Norm to Equal 2h in the Simple Continued Fraction Expansion of
$\sqrt{{{2}^{h}}c}$
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- Journal:
- Canadian Mathematical Bulletin / Volume 48 / Issue 1 / 01 March 2005
- Published online by Cambridge University Press:
- 20 November 2018, pp. 121-132
- Print publication:
- 01 March 2005
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- Article
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We look at the simple continued fraction expansion of
$\sqrt{D}$ for any 
$D\,=\,{{2}^{h}}c$ where 
$c\,>\,1$ is odd with a goal of determining necessary and sufficient conditions for the central norm (as determined by the infrastructure of the underlying real quadratic order therein) to be 
${{2}^{h}}$. At the end of the paper, we also address the case where 
$D\,=\,c$ is odd and the central norm of $\sqrt{D}$ is equal to 2.
