## Problem of the Day #385: A Variation on Fermat’s Last Theorem
*April 7, 2012*

*Posted by Saketh in : potd , trackback*

Alex has been tinkering with an elegant proof of Fermat’s Last Theorem. Although this post is a little too small to contain his proof, he does have for you an alternate equation to consider:

$$ x^x + y^y = 2 \cdot z^z $$

Find, with proof, all ordered triples of positive integers $(x,y,z)$ that satisfy this equation.

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