perplexus.info :: Just Math : Some Powers Sum Power

Some Powers Sum Power (Posted on 2014-03-09)

Determine all possible triplets (A,B,C) of positive integers such that:

                     A^B + B^C = C^A

Prove that there are no others.

No Solution Yet Submitted by K Sengupta

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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

5^1 + 3^3 = 2^5

5+27 = 32

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

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