\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\citation{CohenIannucci03}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction and Results}}{1}{section.1}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Cycles of arbitrary order}}{2}{section.2}}
\newlabel{lem:soroosh}{{2.1}{2}{Cycles of arbitrary order\relax }{lem.2.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces ${\mathaccentV {bar}016a}$ that give rise to an various cycle sizes.}}{4}{table.1}}
\newlabel{tab:cycle}{{1}{4}{Cycles of arbitrary order\relax }{table.1}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Computing $D^{-1}(n)$.}}{4}{section.3}}
\newlabel{sec:Dinverse}{{3}{4}{Computing $D^{-1}(n)$}{section.3}{}}
\newlabel{lem:core}{{3.1}{4}{Computing $D^{-1}(n)$}{lem.3.1}{}}
\newlabel{cor:prime}{{3.1}{4}{Computing $D^{-1}(n)$}{cor.3.1}{}}
\newlabel{cor:odd squarefree}{{3.2}{4}{Computing $D^{-1}(n)$}{cor.3.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces $D_c(n)$ for $n \leq 100$ when $D_c(n)$ is non-empty.}}{5}{table.2}}
\newlabel{tab:top100}{{2}{5}{Computing $D^{-1}(n)$}{table.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Examples of two different Canonical values, for $n \leq 2000$}}{5}{table.3}}
\newlabel{tab:double}{{3}{5}{Computing $D^{-1}(n)$}{table.3}{}}
\citation{Dubner96}
\citation{IndlekoferJarai99}
\citation{Ribenboim91}
\citation{CohenIannucci03}
\bibstyle{plain}
\newlabel{lem:p+1}{{3.2}{6}{Computing $D^{-1}(n)$}{lem.3.2}{}}
\newlabel{lem:coprime}{{3.3}{6}{Computing $D^{-1}(n)$}{lem.3.3}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Conclusions}}{6}{section.4}}
\bibcite{CohenIannucci03}{1}
\bibcite{Dubner96}{2}
\bibcite{IndlekoferJarai99}{3}
\bibcite{Ribenboim91}{4}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{18.01645pt}
\newlabel{tocindent1}{25.06636pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Acknowledgment}}{7}{section.5}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{7}{section*.1}}
