\documentclass[12pt]{article}

\usepackage[margin=0.7in]{geometry}

\usepackage{fancyhdr,lastpage}

\usepackage{amsmath,amsfonts,amssymb,amsthm}
\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{lem}{Lemma}
\newtheorem{conj}{Conjecture}
\newtheorem{cor}{Corollary}
\theoremstyle{definition}
\newtheorem{defn}{Definition}

\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 October 16, 2013}}
\begin{document}
\emph{Let $F_1=1$, $F_2=1$, and $F_n=F_{n-1}+F_{n-2}$ for $n\geq
  3$. Prove that $4\mid F_n$ if and only if $6\mid n$ (hint: prove a
  stronger statement about $F_n$'s equivalency modulo 4 for various
  $n$).}

\begin{prop}
  % Put your stronger proposition here!
\end{prop}
\begin{proof}
  % Proof here!
\end{proof}
\end{document}
