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

1,1

Comments

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

The magic sum is 8515.

Links

Table of n, a(n) for n=1..16.

Paul Pierrat, François Thiriet, and Paul Zimmermann, Magic Squares of Squares.

Philippe Michaud-Rodgers, Magic Squares of Squares.

Ivars Peterson, Magic Squares of Squares.

Example

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 ]

Crossrefs

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

Sequence in context: A140175 A116226 A115446 * A254850 A139410 A031566

Adjacent sequences: A358442 A358443 A358444 * A358446 A358447 A358448

Keyword

nonn,fini,full

Author

Robert C. Lyons, Dec 30 2022

Status

approved