Satanic square

A Satanic square is a more powerful version of a magic square.

Basically, it's a magic square that remains magic after all its numbers are raised to a specific (fixed) power. Satanic squares of small dimensions are not possible to build, the first known square is a 8x8 matrix:

<math> \begin{bmatrix}

 5 & 31 & 35 & 60 & 57 & 34 & 8 & 30 \\

19 & 9 & 53 & 46 & 47 & 56 & 18 & 12 \\ 16 & 22 & 42 & 39 & 52 & 61 & 27 & 1 \\ 63 & 37 & 25 & 24 & 3 & 14 & 44 & 50 \\ 26 & 4 & 64 & 49 & 38 & 43 & 13 & 23 \\ 41 & 51 & 15 & 2 & 21 & 28 & 62 & 40 \\ 54 & 48 & 20 & 11 & 10 & 17 & 55 & 45 \\ 36 & 58 & 6 & 29 & 32 & 7 & 33 & 59 \\ \end{bmatrix} </math>

This square has a sum of 260. Raising every number to its power of two gives the following square:

<math> \begin{bmatrix} 25 & 961 & 1225 & 3600 & 3249 & 1156 & 64 & 900 \\ 361 & 81 & 2809 & 2116 & 2209 & 3136 & 324 & 144 \\ 256 & 484 & 1764 & 1521 & 2704 & 3721 & 729 & 1 \\ 3969 & 1369 & 625 & 576 & 9 & 196 & 1936 & 2500 \\ 676 & 16 & 4096 & 2401 & 1444 & 1849 & 169 & 529 \\ 1681 & 2601 & 225 & 4 & 441 & 784 & 3844 & 1600 \\ 2916 & 2304 & 400 & 121 & 100 & 289 & 3025 & 2025 \\ 1296 & 3364 & 36 & 841 & 1024 & 49 & 1089 & 3481 \\ \end{bmatrix} </math>

Which is a magic square with a sum of 11,180

See also: Magic square, Diabolic square