\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]{}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{setdef}{{1}{2}{Introduction}{equation.1.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}The $\sigma _m$-sequences}{2}{section.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Diophantine equations}{2}{subsection.2.1}}
\newlabel{prel1}{{2.1}{2}{Diophantine equations}{subsection.2.1}{}}
\newlabel{gl1}{{2}{2}{Diophantine equations}{equation.2.2}{}}
\newlabel{mequal1}{{3}{2}{Diophantine equations}{equation.2.3}{}}
\newlabel{mequal2}{{4}{3}{Diophantine equations}{equation.2.4}{}}
\newlabel{DEsigma2}{{5}{3}{Diophantine equations}{equation.2.5}{}}
\newlabel{DEsigma3}{{6}{3}{Diophantine equations}{equation.2.6}{}}
\newlabel{letzte}{{7}{3}{}{equation.2.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Some elementary primality results}{4}{subsection.2.2}}
\newlabel{prel2}{{2.2}{4}{Some elementary primality results}{subsection.2.2}{}}
\newlabel{propo101K}{{5}{4}{}{theorem.5}{}}
\newlabel{propo102K}{{6}{4}{}{theorem.6}{}}
\newlabel{propo103K}{{7}{4}{}{theorem.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Special values of $\sigma _1$}{4}{subsection.2.3}}
\newlabel{subssigma1}{{2.3}{4}{Special values of $\sigma _1$}{subsection.2.3}{}}
\newlabel{lemma101K}{{8}{4}{}{theorem.8}{}}
\newlabel{lemma102K}{{9}{4}{}{theorem.9}{}}
\newlabel{lemma103K}{{10}{4}{}{theorem.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Special values of $\sigma _2$}{5}{subsection.2.4}}
\newlabel{sigma2sec}{{2.4}{5}{Special values of $\sigma _2$}{subsection.2.4}{}}
\newlabel{lemma001K}{{12}{5}{}{theorem.12}{}}
\newlabel{hkabsch}{{8}{5}{Special values of $\sigma _2$}{equation.2.8}{}}
\newlabel{lemma005K}{{13}{5}{}{theorem.13}{}}
\newlabel{kado}{{9}{6}{Special values of $\sigma _2$}{equation.2.9}{}}
\newlabel{cadeau}{{10}{6}{Special values of $\sigma _2$}{equation.2.10}{}}
\newlabel{lemma006K}{{15}{6}{}{theorem.15}{}}
\newlabel{sub1}{{11}{6}{Special values of $\sigma _2$}{equation.2.11}{}}
\newlabel{lemma007K}{{16}{7}{}{theorem.16}{}}
\newlabel{lemma008K}{{17}{7}{}{theorem.17}{}}
\newlabel{sub2}{{12}{7}{Special values of $\sigma _2$}{equation.2.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Some further observations about $\sigma _3$}{8}{subsection.2.5}}
\newlabel{parameterDE3}{{13}{8}{Some further observations about $\sigma _3$}{equation.2.13}{}}
\newlabel{DE3allg}{{14}{8}{Some further observations about $\sigma _3$}{equation.2.14}{}}
\citation{pepin}
\citation{jaroma}
\citation{proth}
\newlabel{propoKK007K}{{19}{9}{}{theorem.19}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Primality testing and generalized Fermat numbers}{9}{section.3}}
\citation{lucas2}
\citation{aigner}
\citation{chaumont1}
\citation{chaumont2}
\citation{krizek1}
\citation{krizek2}
\citation{muller1}
\citation{muller2}
\citation{muller3}
\citation{witno1}
\citation{witno2}
\citation{muller2}
\citation{muller4}
\citation{caldwell}
\citation{cosgrave}
\citation{gulliver}
\citation{kurlberg}
\citation{krizek0}
\citation{berriz}
\citation{grau}
\citation{guthmann}
\citation{muller4}
\newlabel{hauptsatz001K}{{21}{10}{}{theorem.21}{}}
\citation{muller4}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Fermat periods}{11}{subsection.3.1}}
\newlabel{satz001K}{{23}{11}{}{theorem.23}{}}
\newlabel{folg1K}{{25}{11}{}{theorem.25}{}}
\newlabel{folg2K}{{26}{11}{}{theorem.26}{}}
\newlabel{consK}{{27}{12}{}{theorem.27}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}A primality theorem using Fermat periods}{12}{subsection.3.2}}
\newlabel{satz002K}{{29}{12}{}{theorem.29}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Proof of Theorem \ref  {hauptsatz001K}}{12}{subsection.3.3}}
\citation{bjorn}
\bibcite{aigner}{1}
\bibcite{berriz}{2}
\bibcite{bjorn}{3}
\bibcite{caldwell}{4}
\bibcite{chaumont1}{5}
\bibcite{chaumont2}{6}
\@writefile{toc}{\contentsline {section}{\numberline {4}Discussion and open problems}{13}{section.4}}
\bibcite{cosgrave}{7}
\bibcite{grau}{8}
\bibcite{gulliver}{9}
\bibcite{guthmann}{10}
\bibcite{jaroma}{11}
\bibcite{kurlberg}{12}
\bibcite{krizek0}{13}
\bibcite{krizek1}{14}
\bibcite{krizek2}{15}
\bibcite{lucas2}{16}
\bibcite{muller1}{17}
\bibcite{muller2}{18}
\bibcite{muller3}{19}
\bibcite{muller4}{20}
\bibcite{pepin}{21}
\bibcite{proth}{22}
\bibcite{witno1}{23}
\bibcite{witno2}{24}