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\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{lem}{Lemma}
\newtheorem{conj}{Conjecture}
\newtheorem{cor}{Corollary}
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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 4, 2013}}
\begin{document}
\begin{enumerate}
\item \emph{Prove that if $a^2+1=2^n$ for an integer $a$ and integer $n\geq
  1$, then $a$ is odd.}

\begin{proof}
\end{proof}

\item \emph{Use your result from the previous part to prove that there are
  no integer solutions to $a^2+1=2^n$ for $n\geq 2$.}

\begin{proof}
\end{proof}

\item \emph{Prove that $x^3+x^2-1=0$ has a unique real solution between
  $x=\frac23$ and $x=1$.}

\begin{proof}
\end{proof}
\end{enumerate}
\end{document}
