\relax \providecommand\hyper@newdestlabel[2]{} \citation{bec07} \@writefile{toc}{\contentsline {chapter}{\numberline {21}Number theory}{197}{chapter.21}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {21.1}Primes and factors}{197}{section.21.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Number of primes}{198}{section.21.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Density of primes}{198}{section.21.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Conjectures}{199}{section.21.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Basic algorithms}{199}{section.21.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Sieve of Eratosthenes}{200}{lstnumber.-191.11}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Euclid's algorithm}{200}{lstnumber.-192.6}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Euler's totient function}{201}{lstnumber.-193.4}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {21.2}Modular arithmetic}{201}{section.21.2}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Modular exponentiation}{202}{section.21.2}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Fermat's theorem and Euler's theorem}{202}{lstnumber.-194.7}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Modular inverse}{202}{lstnumber.-194.7}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Computer arithmetic}{203}{lstnumber.-194.7}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {21.3}Solving equations}{204}{section.21.3}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Chinese remainder theorem}{205}{section.21.3}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {21.4}Other results}{205}{section.21.4}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Lagrange's theorem}{205}{section.21.4}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Zeckendorf's theorem}{206}{section.21.4}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Pythagorean triples}{206}{section.21.4}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{Wilson's theorem}{206}{section.21.4}\protected@file@percent } \@setckpt{chapter21}{ \setcounter{page}{207} \setcounter{equation}{0} \setcounter{enumi}{5} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{1} \setcounter{mpfootnote}{0} \setcounter{part}{3} \setcounter{chapter}{21} \setcounter{section}{4} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{0} \setcounter{table}{0} \setcounter{lstnumber}{3} \setcounter{Item}{7} \setcounter{Hfootnote}{37} \setcounter{bookmark@seq@number}{109} \setcounter{parentequation}{0} \setcounter{fileFrom}{0} \setcounter{rankFrom}{0} \setcounter{fileTo}{0} \setcounter{rankTo}{0} \setcounter{ps@inverse}{0} \setcounter{ps@knightangle}{0} \setcounter{halfmove}{0} \setcounter{move}{0} \setcounter{helpgobble}{0} \setcounter{helpnumber}{0} \setcounter{helpnumberMove}{0} \setcounter{idxcols}{2} \setcounter{lstlisting}{0} \setcounter{section@level}{0} }