Each of A, B, C and D is a nonzero integer such that:

A

^{2} + B

^{2} + C

^{2} = D

^{4}, and:

A + B + C = D

^{2}
Find the four smallest values of abs(A) + abs(B) + abs(C)

__Note__: abs(x) is the

** Absolute Value Function**
(In reply to

computer solution -- the 33 lowest. by Charlie)

Oh, right!

You can get a solution by multiplying any solution by a perfect square. I missed that.

I did get (54, 54, -27) by multiplying (6, 6, -3) by 9, because the terms added up to 9. But I didn't see that that I could also multiply it by 4, to get (24, 24, -12).

Thanks, Charlie