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Quadratic and Quartic Query (Posted on 2015-09-06) Difficulty: 3 of 5
Each of A, B, C and D is a nonzero integer such that:

A2 + B2 + C2 = D4, and:
A + B + C = D2

Find the four smallest values of abs(A) + abs(B) + abs(C)

Note: abs(x) is the Absolute Value Function

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: computer solution -- the 33 lowest. Comment 3 of 3 |
(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

  Posted by Steve Herman on 2015-09-06 16:00:19
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