a | b | c | d | |
|---|---|---|---|---|
a | a2 | ab | ac | ad |
b | ab | b2 | bc | bd |
c | ac | bc | c2 | cd |
d | ad | bd | cd | d2 |
Where a, b, c, and d are the numbers 0, 1, 2, ...,8, 9. The box a2 =axa, b2=bxb, ab=axb, ..., d2=dxd.
Now we are going to add the numbers in the box diagonally, starting with the lower right-hand box. Add the 2nd box next diagonal row up, ..., and do the same until the last box. Therefore, we obtained the following formula,
(abcd)2=a2|2xaxb|2xaxc+b2|2xbxc+2xaxd|2xbxd+c2|2xcxd|d2 (1)
Example1,
(1235)2=12|2x1x2|2x1x3+22|2x2x3+2x1x5|2x2x5+32|2x3x5|52
=1|4|10|22|29|30|25=1525225
(2489)2=22|2x2x4|2x2x8+42|2x4x8+2x2x9|2x4x9+82|2x8x9|92
=4|16|48|100|136|144|81=6195121
(8236)2=64|32|52|108|33|36|36=67831696