\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{BBP} \citation{Bailey_Crandall} \citation{Bailey} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}} \citation{BBP} \citation{BBP} \citation{Bailey} \@writefile{toc}{\contentsline {section}{\numberline {2}Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes}{2}{section.2}} \newlabel{big_frac}{{1}{2}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.1}{}} \newlabel{Borwein_eq}{{2}{2}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.2}{}} \newlabel{factoring}{{3}{3}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.3}{}} \newlabel{Mobius}{{4}{3}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.4}{}} \newlabel{pow2}{{5}{3}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.5}{}} \newlabel{root2_eq}{{6}{3}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.6}{}} \citation{Bailey} \newlabel{root3_eq}{{7}{4}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.7}{}} \citation{BBP} \citation{BBG} \newlabel{GMP-form}{{8}{5}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.8}{}} \citation{Brillhart} \citation{Schinzel} \citation{Stevenhagen} \citation{Brent} \citation{Bailey} \newlabel{GMP}{{9}{6}{Cyclotomic Polynomials and Generalized Gaussian-Mersenne Primes\relax }{equation.9}{}} \@writefile{toc}{\contentsline {section}{\numberline {3}Aurifeuillian Factorizations}{6}{section.3}} \citation{Schinzel} \newlabel{theo_cyclotomic}{{3.1}{7}{Aurifeuillian Factorizations\relax }{thm.3.1}{}} \newlabel{main}{{10}{7}{Aurifeuillian Factorizations\relax }{equation.10}{}} \newlabel{ex1}{{11}{8}{Aurifeuillian Factorizations\relax }{equation.11}{}} \newlabel{AF1}{{12}{8}{Aurifeuillian Factorizations\relax }{equation.12}{}} \newlabel{ex2}{{13}{8}{Aurifeuillian Factorizations\relax }{equation.13}{}} \bibcite{Bailey}{1} \bibcite{BBP}{2} \bibcite{Bailey_Crandall}{3} \bibcite{BBG}{4} \bibcite{Brent}{5} \bibcite{Brillhart}{6} \bibcite{Schinzel}{7} \bibcite{Stevenhagen}{8}