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is a magic square,

Can you find a number such that

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If we define and the magic square contains the terms

From this the remaining terms follow, due to the requirement that each row and column sum to

Imagine a magic square comprised entirely of square integers.

That would be the holy grail of magic squares of squares if we could find that, if one exists (m), it is estimated to be over 15 digits in length.

P.

For the smallest magic square, must be odd, and all other squares are odd. Since we want the square entries to be distinct, we need to choose so that can be expressed in at least four distinct ways as the sum of two squares

It has been shown that the magic square of squares has the form

a² b² c² x+y, x-y-z, x+z

d² e² f² = x-y+z, x, x+y-z

g² h² i² x-z, x+y+z, x-y

and that x*y*z*(y+z)*(y-z) has to be divisible by 1546645545467664981281303961600. which is all primes <=67 except 59.

I’ll revisit the problem at a later time