Bimagic Square

In mathematics, a bimagic square is a magic square that also remains magic if all of the numbers it contains are squared. The first known bimagic square has order 8 and magic constant 260; it has been conjectured that no nontrivial bimagic squares of order less than 8 exist, but the conjecture remains unproven. However, J. R. Hendricks was able to show in 1998 that no bimagic square of order 3 exists, save for the trivial bimagic square containing the same number nine times.
\begin{bmatrix} 
  16 & 41 & 36 & 5 & 27 & 62 & 55 & 18 \\  26 & 63 & 54 & 19 & 13 & 44 & 33 & 8 \\  1 & 40 & 45 & 12 & 22 & 51 & 58 & 31 \\  23 & 50 & 59 & 30 & 4 & 37 & 48 & 9 \\  38 & 3 & 10 & 47 & 49 & 24 & 29 & 60 \\  52 & 21 & 32 & 57 & 39 & 2 & 11 & 46 \\  43 & 14 & 7 & 34 & 64 & 25 & 20 & 53 \\  61 & 28 & 17 & 56 & 42 & 15 & 6 & 35
\end{bmatrix}

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