September 20th, 2011, 05:38 AM  #1 
Newbie Joined: Sep 2011 Posts: 18 Thanks: 0  Exponents  conditions
Hi! As I was solving a math problem (an equation with exponents) I found myself unable to go any further without having determined what conditions must be met by integers so that . I can post the original quetion, if needed. Thanks, Arnold 
September 20th, 2011, 06:01 AM  #2 
Member Joined: Apr 2010 Posts: 65 Thanks: 0  Re: Exponents  conditions 
September 20th, 2011, 06:48 AM  #3  
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: Exponents  conditions Quote:
It's clear that m > n, else the left side will not be positive. Further, n = 0 else the left side will be a multiple of 5. So the problem becomes But then you have two consecutive powers which can only happen if a base or exponent is 0 or 1, or else if the numbers are 8 and 9, by Catalan's conjecture (now a theorem). Cannon, meet fly.  
September 20th, 2011, 08:10 AM  #4 
Newbie Joined: Sep 2011 Posts: 18 Thanks: 0  Re: Exponents  conditions
Thanks a lot!

September 20th, 2011, 08:38 AM  #5 
Newbie Joined: Sep 2011 Posts: 18 Thanks: 0  Re: Exponents  conditions
Could you explain it to me why n=0? How do I prove it?

September 20th, 2011, 08:46 AM  #6 
Newbie Joined: Sep 2011 Posts: 18 Thanks: 0  Re: Exponents  conditions
I mean, I understand why n=0. I just want to know if it can be proven somehow.

September 20th, 2011, 08:56 AM  #7  
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: Exponents  conditions Quote:
 
September 20th, 2011, 08:59 AM  #8 
Newbie Joined: Sep 2011 Posts: 18 Thanks: 0  Re: Exponents  conditions
Ok, thanks. So I don't need to apply modulo, etc, do I?

September 20th, 2011, 10:40 AM  #9  
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: Exponents  conditions Quote:
 

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