OFFSET
1,1
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).
EXAMPLE
The magic square is
+-------+-------+-------+
| 187^2 | 17^4 | 7585 |
+-------+-------+-------+
| 11^4 | 205^2 | 69409 |
+-------+-------+-------+
| 76465 | 23^2 | 49081 |
+-------+-------+-------+
CROSSREFS
KEYWORD
nonn,fini,full,tabf
AUTHOR
Arkadiusz Wesolowski, Sep 23 2018
STATUS
approved