\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\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{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\citation{Malderen}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{eq.1-1}{{1}{1}{Introduction}{equation.1.1}{}}
\citation{Euler}
\newlabel{eq.1-2}{{2}{2}{Introduction}{equation.1.2}{}}
\newlabel{eq.1-3}{{3}{2}{Introduction}{equation.1.3}{}}
\newlabel{thm.0}{{1.1}{2}{}{theorem.1.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Some Properties of $D_n(a_k)$}{3}{section.2}}
\newlabel{eq.2-1}{{5}{3}{}{equation.2.5}{}}
\newlabel{eq.2-2}{{6}{3}{Some Properties of $D_n(a_k)$}{equation.2.6}{}}
\newlabel{cor.2-2}{{2.2}{3}{}{theorem.2.2}{}}
\newlabel{thm.2-3}{{2.3}{3}{}{theorem.2.3}{}}
\newlabel{eq.2-3}{{7}{3}{}{equation.2.7}{}}
\newlabel{pro.2-4}{{2.4}{4}{}{theorem.2.4}{}}
\newlabel{eq.2-4}{{8}{4}{}{equation.2.8}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Applications}{4}{section.3}}
\newlabel{thm.3-1}{{3.1}{4}{}{theorem.3.1}{}}
\newlabel{eq.3-1}{{9}{4}{}{equation.3.9}{}}
\newlabel{eq.3-2}{{10}{4}{}{equation.3.10}{}}
\citation{AS}
\citation{Malderen}
\citation{Chen}
\newlabel{eq.3-3}{{11}{5}{Applications}{equation.3.11}{}}
\newlabel{eq.3-4}{{12}{5}{Applications}{equation.3.12}{}}
\citation{GKP}
\citation{HC}
\newlabel{cor.3-2}{{3.2}{6}{}{theorem.3.2}{}}
\newlabel{eq.3-5}{{13}{6}{}{equation.3.13}{}}
\newlabel{eq.3-6}{{14}{6}{}{equation.3.14}{}}
\newlabel{thm.3-3}{{3.3}{6}{}{theorem.3.3}{}}
\newlabel{eq.3-8}{{15}{6}{}{equation.3.15}{}}
\newlabel{eq.3-9}{{16}{6}{}{equation.3.16}{}}
\citation{Roman}
\newlabel{eq.3-10}{{17}{7}{Applications}{equation.3.17}{}}
\newlabel{cor.3-4}{{3.4}{7}{}{theorem.3.4}{}}
\newlabel{eq.3-11}{{19}{7}{}{equation.3.19}{}}
\newlabel{thm.3-5}{{3.5}{7}{}{theorem.3.5}{}}
\newlabel{eq.3-13}{{20}{7}{}{equation.3.20}{}}
\newlabel{eq.3-14}{{21}{7}{}{equation.3.21}{}}
\newlabel{eq.3-15}{{22}{7}{}{equation.3.22}{}}
\citation{GKP}
\citation{BES}
\newlabel{thm.3-6}{{3.6}{8}{}{theorem.3.6}{}}
\newlabel{eq.3-16}{{23}{8}{}{equation.3.23}{}}
\newlabel{eq.3-17}{{24}{8}{}{equation.3.24}{}}
\newlabel{eq.3-18}{{25}{8}{Applications}{equation.3.25}{}}
\bibcite{AS}{1}
\bibcite{Euler}{2}
\bibcite{HC}{3}
\bibcite{Chen}{4}
\bibcite{GKP}{5}
\bibcite{Malderen}{6}
\bibcite{Roman}{7}
\bibcite{BES}{8}
\newlabel{eq.3-19}{{26}{9}{Applications}{equation.3.26}{}}