\begin{definition}[Definition:Magic Square]
A '''magic square''' is an arrangement of $n^2$ numbers into an $n \times n$ square array such that:
:the sum of the elements of each row
:the sum of the elements in each column
:the sum of the elements along each diagonal
are the same.
When the elements are not specified, it is conventional for them to be the first $n^2$ (strictly) positive integers.
\end{definition}