\begin{definition}[Definition:International Standard Book Number/ISBN-13]
An '''international standard book number''' is an index number used to uniquely identify a published [https://en.wikipedia.org/wiki/Book book].
The '''ISBN-$13$''' format consists of a string of $12$ digits followed by a check digit.
The check digit $d$ is calculated as:
:$d = \ds \sum_{k \mathop = 1}^{12} k d_k \pmod {10}$
\end{definition}