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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 25, 2013}}
\begin{document}
\emph{\textbf{Prove or disprove} each of the following statements:}
\begin{enumerate}
\item \emph{For the Fibonacci sequence as defined elsewhere in this
    class (i.e. $F_1=1$, $F_2=1$, and $F_n=F_{n-1}+F_{n-2}$ for $n\geq
    3$), it is the case that for all natural numbers $n$, $F_n$ and
    $F_{n+1}$ are relatively prime.}


\item \emph{For all natural numbers $a$, $b$, and $c$, if
    $\gcd(a,b)=\gcd(b,c)$, then $\gcd(a,b)=\gcd(a,c)$.}


\end{enumerate}
\end{document}
