perplexus.info :: Just Math : An equation

An equation (Posted on 2014-07-03)

The equation x^xy^y=z^z has trivial integer solutions if x=1 or y=1. What is the smallest solution to x^xy^y=z^z where x, y, and z are integers and 1<x≤y?

No Solution Yet Submitted by Math Man

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re(2): solution

Comment 5 of 5 |

(In reply to re: solution by broll)

Yes, I mistakenly used '+' when I should have used '*'.

Instead, (az)^a * (bz)^b = z

and a^a * b^b * z^(a+b-1) = 1

requiring a=b=1 and z=1.

Posted by xdog on 2014-07-14 10:33:23

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