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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 28, 2013}}
\begin{document}
\begin{enumerate}
\item \emph{Prove that, for any nonconstant polynomial $f(x)$ with
    non-negative integer coefficients, there is a natural number $n$
    such that $f(n)$ is composite. (Historical note: people have
    proposed ``prime-finding'' functions like $f(x)=x^2+x+41$; this
    proof demonstrates that no polynomial function generates only
    primes)}

  \begin{proof}
    
  \end{proof}

\item \emph{Find the smallest number with exactly 12 natural-number factors
  (including itself and 1). Show your work!}
\end{enumerate}
\end{document}
