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\title{Continued Fractions and the GCD}
\author{Robert M. Corless}
\date{\today}
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\samepage \begin{eqnarray*}\frac{r_{k-1}}{r_{k}} &=& \frac{n_k r_k + r_{k+1}}{r_k} \\
&=& n_k + \frac{1}{r_k/r_{k+1}} \\
&=& n_k + \frac{1}{n_{k+1} + \frac{1}{\ddots}}
\end{eqnarray*}
}
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\samepage \setbox\sizebox=\hbox{$( \log_\tau(\sqrt{5}N)) - 2$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline49: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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\samepage \setbox\sizebox=\hbox{$\tau = (1+\sqrt{5})/2$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline51: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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\samepage \setbox\sizebox=\hbox{$r_{n-1} = q r_{n} + r_{n+1}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline57: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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