May 14th, 2013, 10:57 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, 05:02 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 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.


Tags 
diophantine, equations 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Exponential diophantine equations  Drake  Number Theory  8  September 10th, 2013 01:59 PM 
Some observations about diophantine equations  mathbalarka  Number Theory  0  April 24th, 2012 09:50 PM 
Twin primes and Diophantine equations  ibougueye  Number Theory  18  March 24th, 2012 06:37 PM 
Fun Diophantine Equations  icemanfan  Number Theory  1  March 14th, 2012 02:52 PM 
Solving Diophantine equations  MyNameIsVu  Number Theory  0  April 7th, 2009 09:54 PM 