Magic Square of Squares

A square is magic if each of the rows, columns, and diagonals add up to the same total.  So, for example, the square

    25    4  19

    10   16  22

    13   28   7 

is magic, since every row, column, and diagonal adds up to 48.  Of the nine entries, three (4, 16 and 25) are perfect squares.

The problem is to find a 3 by 3 magic square all of whose entries are distinct perfect squares, or prove that such a square cannot exist.

For further information, please see:

[1]  http://www.multimagie.com/indexengl.htm

[2] http://cboyer.club.fr/multimagie/English/SquaresOfSquares.htm

[3] http://www.rose-hulman.edu/mathjournal/archives/2003/vol4-n1/paper3/v4n1-3pd.pdf

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