README4.TXT : TETRAMAGIC SQUARE
by Christian Boyer and Andr Viricel, France, june 2001.
	www.multimagie.com
	cboyer@club-internet.fr
Modified slightly for English grammer by Harvey Heinz, April 8, 2002.


The size of the square is 512x512, and has the following properties :

- each number from 0 to 262,143 is present once and only once
  if not, it would be very easy to build magic squares ;-)		
- the square is magic : the sums of the cells of the 512 lines, 512 columns and 2 diagonals
  are all equal to S1
- the square is bimagic : the sums of the squares of the cells of the 512 lines, 512 columns and 2 diagonals
  are all equal to S2
- the square is trimagic : the sums of the cubes of the cells of the 512 lines, 512 columns and 2 diagonals
  are all equal to S3
- the square is tetramagic : the sums of the 4th powers of the cells of the 512 lines, 512 columns and 2 diagonals
  are all equal to S4

As a "bonus", the square has the following supplemental property :
- the sums of the 5th powers of the cells of the 512 lines are all equal to S5

The magic sums S1 to S5 are :

	S1 =	67108608	
	S2 =	11728056920832	
	S3 =	2305825417061203968	
	S4 =	483565716171561366524160	
	S5 =	105636341097042573844228866048	

The ASCII file named CARRE4.TXT contains the 262,144 numbers of the square stored this way :

	a(0,0)
	a(0,1)
	a(0,2)
	...
	a(0,511)
	a(1,0)
	a(1,1)
	a(1,2)
	...
	a(511,511)

For more details, see the article published in Pour La Science August 2001, or see www.multimagie.com.
