# 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 ...*