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Bimagic Square, Trimagic Square

Bimagic Square

Some magic squares are spectacular. In addition to the normal properties of constant sum over rows, columns, and the main diagonals, some remains to be a magic square when every entry is squared. (1,2,3..n^2 replaced by 1,4,9..n^4). This is known as bimagic square. As an example, a pandiagonal bimagic square of order eight is shown.

47 28  6 49 23 36 62  9
 8 51 45 26 64 11 21 34
53  2 32 43 13 58 40 19
30 41 55  4 38 17 15 60
42 29  3 56 18 37 59 16
 1 54 44 31 57 14 20 39
52  7 25 46 12 63 33 22
27 48 50  5 35 24 10 61

Trimagic Square

We can go furthur! A trimagic square is a magic square which remains to be magic when every number is squared/cubed. One may not believe that such perculiarity really exist!

example in progres

Can we construct quadmagic, pentmagic.. square?

To be continued ...