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\documentclass{article}
\usepackage{geometry}
\usepackage{fancyhdr}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{graphicx}
\usepackage{hyperref}
\usepackage{lipsum}
\title{Test document}
\author{Your name \\ \url{you@example.com}}
\date{2009-Oct-12}
\begin{document}
\maketitle
\tableofcontents
\newpage
This is some preamble text that you enter
yourself.\footnote{First footnote.}\footnote{Second footnote.}
\section{Text for the first section}
\lipsum[1]
\subsection{Text for a subsection of the first section}
\lipsum[2-3]
\label{labelone}
\subsection{Another subsection of the first section}
\lipsum[4-5]
\label{labeltwo}
\section{The second section}
\lipsum[6]
Refer again to \ref{labelone}.\cite{ConcreteMath}
Note also the discussion on page \pageref{labeltwo}
\subsection{Title of the first subsection of the second section}
\lipsum[7]
There are $\binom{2n+1}{n}$ sequences with $n$ occurrences of
$-1$ and $n+1$ occurrences of $+1$, and Raney's lemma
tells us that exactly $1/(2n+1)$ of these sequences have all
partial sums positive.
Elementary calculus suffices to evaluate $C$ if we are clever enough
to look at the double integral
\begin{equation*}
C^2
=\int_{-\infty}^{+\infty} e^{-x^2} \mathrm{d}x
\int_{-\infty}^{+\infty} e^{-y^2} \mathrm{d}y\;.
\end{equation*}
Solve the following recurrence for $n,k\geq 0$:
\begin{align*}
Q_{n,0} &= 1
\quad Q_{0,k} = [k=0]; \\
Q_{n,k} &= Q_{n-1,k}+Q_{n-1,k-1}+\binom{n}{k}, \quad\text{for $n,k>0$.}
\end{align*}
Therefore
\begin{equation*}
a\equiv b\pmod{m}
\qquad\Longleftrightarrow\qquad
a\equiv b \pmod{p^{m_p}}\quad\text{for all $p$}
\end{equation*}
if the prime factorization of $m$ is $\prod_p p^{m_p}$.
\begin{thebibliography}{9}
\bibitem{ConcreteMath}
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik,
\textit{Concrete mathematics},
Addison-Wesley, Reading, MA, 1995.
\end{thebibliography}
\end{document}
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