## Problem of the Day #385: A Variation on Fermat’s Last TheoremApril 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.