Use the \label
, \ref
mechanism; once you have \label
led the equation you can use \ref
inside \tag
to retrieve the number:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}\label{eq:test}
a = b + c.
\end{equation}
\begin{equation}
a = b + c. \tag{\ref{eq:test}}
\end{equation}
\end{document}

As Niel de Beaudrap mentions in his comment, one way to avoid equation numbering confusion for the reader would be to add "revisited" to the tag of the duplicated equation:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}\label{eq:test}
a = b + c.
\end{equation}
\begin{equation}
a = b + c. \tag{\ref{eq:test} revisited}
\end{equation}
\end{document}

Small addition:
Use equation*
in stead of equation
when repeating the number so that LaTeX knows it should not use a new number. This avoids warnings when using e.g. the hyperref
package. Thus:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}\label{eq:test}
a = b + c.
\end{equation}
\begin{equation*}
a = b + c. \tag{\ref{eq:test} revisited}
\end{equation*}
\end{document}