Find all pairs (x, y) of positive integers such that:
Each of x2+197y/2 and y2+197x/2 is a perfect square.
Let x^2 + 197y/2 = A^2 and
Let y^2 + 197x/2 = B^2
(x, y)
(3840, 15754), A=4037.0, B=15766.0)
(4802, 4802), A=4851.0, B=4851.0)
(18930, 62146), A=19091.0, B=62161.0)
I have not ruled out other solutions where x,y, or both are larger than 100,000.
-----
big = 100000
for x in range(1,big):
for y in range(x,big):
if issquare(x**2+197*y/2) and issquare(y**2+197*x/2):
print('({}, {}), A={}, B={}) '.format(x,y, (x**2+197*y/2)**.5, (y**2+197*x/2)**.5))
|
|
Posted by Larry
on 2023-11-07 23:15:02 |
Some solutions
