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Some Powers Sum Power (Posted on 2014-03-09) Difficulty: 3 of 5
Determine all possible triplets (A,B,C) of positive integers such that:
                     AB + BC = CA
Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Near Misses | Comment 1 of 3
Well, maybe not so near

1^1 + 1^2 = 2^1 
(1+1 = 2), so (1,1,2) works

But not

1^2 + 2^3 = 3^2
1 + 8 = 9

or

5^1 + 3^3 = 2^5
5+27 = 32

  Posted by Steve Herman on 2014-03-09 11:15:42
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