Is there (x,y,z); x^x + y^y = z^z ?

 
 
Do there exist different positive integers   x,   y,   and   z   such that

                   x^x \; + \; y^y \; = \; z^z

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

3 Responses to Is there (x,y,z); x^x + y^y = z^z ?

  1. paul says:

    There are no integers that satisfy that equation. Lets say xy, lets say that z=y+1 and for x^x + y^y to be as big as possible x=y-1, rearranging we have (y+1)^y+1 -[(y^y + (y-1)^y-1] and when y=1 it is indeterminate and for all y>1 it is greater than 0 therefore no matter what x and y are z^z will always be greater.

    Paul.

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