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Power Equality Poser (Posted on 2015-03-29) Difficulty: 3 of 5
Find all nonzero integer solutions of this system of equations:

AA+B= B12 and, BA+B = A3

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Quadratically | Comment 2 of 4 |
After step 4 in the previous post, we know that

A + B = 6 and A = +/- B^2

If A = B^2, then B^2 + B - 6 = 0, making B either -3 or 2.
If A = -B^2, then B^2 - B + 6 = 0, and this has no real solutions.

So there are only two solutions in addition to (1,1), and these are (9,-3) and (4,2).

  Posted by Steve Herman on 2015-03-29 19:03:39
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