Mathematical model for magic square

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As I spent some time on magic squares, it seems like the magic squares can be formed only with a odd number of rows/columns? Is it that.? If so why? is there a mathematical model that explains magic square?

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It's not true that magic squares can only be formed with an odd number of rows and columns. For instance, consider $$\begin{matrix} 7 & 12 & 1 & 14 \\ 2 & 13 & 8 & 11 \\ 16 & 3 & 10 & 5 \\ 9 & 6 & 15 & 4 \end{matrix}$$ There are more examples, together with some explanations, on the Wikipedia page.