Geodesic
Necessary and Sufficient Conditions for the Central Norm to Equal 2h in the Simple Continued Fraction Expansion of $\sqrt{{{2}^{h}}c}$
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 121-132

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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.
DOI : 10.4153/CMB-2005-011-0
Mots-clés : 11A55, 11D09, 11R11, quadratic Diophantine equations, simple continued fractions, norms of ideals, infrastructure of real quadratic fields 
Mollin, R. A. Necessary and Sufficient Conditions for the Central Norm to Equal 2h in the Simple Continued Fraction Expansion of $\sqrt{{{2}^{h}}c}$. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 121-132. doi: 10.4153/CMB-2005-011-0
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