\documentclass[12pt]{article}

\usepackage[margin=0.7in]{geometry}

\usepackage{fancyhdr,lastpage}

\usepackage{amsmath,amsfonts,amssymb,amsthm}

% We'll define several "theorem" environments.
\newtheorem{prop}{Proposition}
\newtheorem{lem}{Lemma}
\newtheorem{thm}{Theorem}
\pagestyle{fancy}

\lhead{MATH 311-01}
\chead{Problem of the Day}
\rhead{YOUR NAME HERE}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{\textbf{due September 23, 2013}}
\begin{document}
\begin{enumerate}

  % Note a new form: \mid for divisibility and \nmid for
  % indivisibility. You could use "|" instead of "\mid", but the
  % spacing isn't very good. And note that "\not|" and "\not\mid" look
  % _terrible_, since the negation slash for a divisibility pipe runs
  % at a different angle than the standard negation slash.
\item \emph{For integers $x$ and $y$, prove that if $3\nmid x$ and
    $3\nmid y$, then $3\mid (x^2-y^2)$.}

  \begin{proof}
%    Your answer here!
  \end{proof}

\item \emph{Let $n$ be a natural number. Prove that if $n\geq14$, then
    there are nonnegative integers $a$ and $b$ such that $n=7a+3b$.}

  \begin{proof}
%    Your answer here!
  \end{proof}
\end{enumerate}
\end{document}
