A358445 Euler's 4 X 4 magic square of squares.

4624, 841, 1681, 1369, 289, 961, 6241, 1024, 3481, 784, 529, 3721, 121, 5929, 64, 2401

Offset: 1

Author

Robert C. Lyons, Dec 30 2022

Keywords

• nonn
• fini
• full

Comments

This is the first known magic square of squares; Euler sent it to Lagrange in 1770.

The magic sum is 8515.

Examples

			The magic square is:
 [ 4624  841 1681 1369 ]
 [  289  961 6241 1024 ]
 [ 3481  784  529 3721 ]
 [  121 5929   64 2401 ]
Equivalently:
 [ 68^2 29^2 41^2 37^2 ]
 [ 17^2 31^2 79^2 32^2 ]
 [ 59^2 28^2 23^2 61^2 ]
 [ 11^2 77^2  8^2 49^2 ]
		

Links

• Paul Pierrat, François Thiriet, and Paul Zimmermann, Magic Squares of Squares.
• Philippe Michaud-Rodgers, Magic Squares of Squares.
• Ivars Peterson, Magic Squares of Squares.

Crossrefs

Cf. A271580: magic sums of 4 X 4 magic squares composed of squares.