A319589 A 3 X 3 magic square with five square entries, read by rows.

34969, 83521, 7585, 14641, 42025, 69409, 76465, 529, 49081

Offset: 1

Author

Arkadiusz Wesolowski, Sep 23 2018

Keywords

• nonn
• fini
• full
• tabf

Comments

Some magic squares of order 3 with five square entries have this parametric form:

|-----------------------|-----------------------|-----------------------|

| (x*y)^2 | y^4 |sqrt(z)*(3*x^2 - y^2)/2|

|-----------------------|-----------------------|-----------------------|

| x^4 | z | 2*z - x^4 |

|-----------------------|-----------------------|-----------------------|

|sqrt(z)*(3*y^2 - x^2)/2| 2*z - y^4 | 2*z - (x*y)^2 |

|-----------------------|-----------------------|-----------------------|

where z = (x^2 + y^2)^2/4, x and y are integers such that (x^4 - y^4 + 2*(x*y)^2)/2 is a square (e.g., x = 11 and y = 17; x = 5337 and y = 6257).

This sequence presents the magic square belonging to this family and having the smallest possible magic sum (S = 126075).

Examples

			The magic square is
+-------+-------+-------+
| 187^2 |  17^4 |  7585 |
+-------+-------+-------+
|  11^4 | 205^2 | 69409 |
+-------+-------+-------+
| 76465 |  23^2 | 49081 |
+-------+-------+-------+
		

Links

• Index entries for sequences related to magic squares

Crossrefs

Cf. A221669, A268855.