May 14th, 2013, 11:57 PM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Diophantine Equations
Can it be proved that there are no solutions to the equation Where (x, y, z) > (1, 1, 1) ? Balarka . 
May 15th, 2013, 06:02 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Diophantine Equations
Yes, f(t) = t^t grows too quickly to have sums. Let x <= y <= z1, then x^x = z^(z1) * (z  ((z1)/z)^(z1)) > z^(z1) * (z  1) > y^y * (z1), a contradiction for y >= 1.


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