perplexus.info :: Just Math : Quadratic and Quartic Query

Quadratic and Quartic Query (Posted on 2015-09-06)

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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