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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 September 25, 2013}}
\begin{document}
% New symbols in this problem: \equiv, which is a triple equals sign,
% and \pmod{...}, which includes parentheses around "mod ...". Note
% that, as previously with arguments of LaTeX commands, when the
% modulus is a single character, as in the case of "\pmod 4", we don't
% actually need braces around the argument. When it's several
% characters we do, as in the case of "\pmod{16}".
\emph{For even integers $x$ and $y$, prove that $x^2\equiv
  y^2\pmod{16}$ \emph{if and only if} either both $x\equiv0\pmod 4$
  and $y\equiv 0\pmod 4$ or both $x\equiv2\pmod 4$ and $y\equiv 2\pmod
  4$.}

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