Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $sqrt{2^hc}$ for Any Odd $c>1$
[摘要] We look at the simple continued fraction expansion of $sqrt{D}$ for any $D=2^hc $ where $c>1$ is odd with a goal of determining necessary andsufficient 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 $2$.
[发布日期] [发布机构]
[效力级别] [学科分类] 数学（综合）
[关键词] quadratic Diophantine equations;simple continued fractions;norms of ideals;infrastructure of real quadratic fields [时效性]
