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\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{lem}{Lemma}
\newtheorem{conj}{Conjecture}
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\lhead{MATH 311-01}
\chead{Problem of the Day}
\rhead{YOUR NAME HERE}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{\textbf{due October 23, 2013}}
\begin{document}
\begin{enumerate}
\item \emph{Prove that for all positive integers $a$, $b$, and $c$,
  $\gcd(\gcd(a,b),c)=\gcd(a,\gcd(b,c))$.}

\item \emph{Find an example of positive integers $a$, $b$, $c$, and $d$ such
  that the six values $\gcd(a,b)$, $\gcd(a,c)$, $\gcd(a,d)$,
  $\gcd(b,c)$, $\gcd(b,d)$, and $\gcd(c,d)$ are all different.}
\end{enumerate}
\end{document}
