May 31st, 2013, 10:14 PM  #11  
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: A new approach to Fermat's last theorem Quote:
 
May 31st, 2013, 10:48 PM  #12  
Senior Member Joined: Apr 2013 Posts: 425 Thanks: 24  Re: A new approach to Fermat's last theorem Quote:
You're right!Thousands of excuses! Adjustment:If and the natural numbers then necessarily are the sides of a triangle.In fact even for my assertion is valid and bviously . Thank you very much!  
June 1st, 2013, 03:54 AM  #13 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: A new approach to Fermat's last theorem
I'm not sure what the '*' is doing in 'N*'. Surely you don't mean that any three natural numbers form the sides of a triangle. You can't, for instance, adjust angles to make a triangle with sides 1, 2 and 10,000, just to take one screamingly obvious example. So what numbers are you talking about?

June 1st, 2013, 03:58 AM  #14 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: A new approach to Fermat's last theorem
Clearly, if x, y and z are integers, or ANY numbers, where x?y?z and xyz forms a triangle, then for sure z<x+y

June 1st, 2013, 04:33 AM  #15 
Senior Member Joined: May 2013 Posts: 118 Thanks: 10  Re: A new approach to Fermat's last theorem
What about FLT?

June 1st, 2013, 04:45 AM  #16  
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: A new approach to Fermat's last theorem Quote:
 
June 4th, 2013, 11:11 AM  #17  
Senior Member Joined: May 2013 Posts: 118 Thanks: 10  Re: A new approach to Fermat's last theorem Quote:
Comparing ( to the already known relation (9) we observe that in ( a has replaced c and ab has replaced a.By (9) we had cocnluded (see step 2,subcases ?a and ?b): and therefore,in a totally analogous way we can conclude now: and thus: r\:Nb \rightarrow \:a=0\r\:b=0" /> absurdity  
June 6th, 2013, 09:46 PM  #18 
Newbie Joined: Jun 2013 Posts: 6 Thanks: 0  Re: A new approach to Fermat's last theorem
I HAVE FOUND A COUNTEREXAMPLE TO WHAT YOU SAY. IF N=7 THEN THE TRIPLE (a,b,c)=(1,2,3) SATISFIES ALL YOYR CRITERIA SO MY QUESTION IS : IF X,Y AND Z DON'T EXIST, HOW CAN THEIR REMAINDERS EXIST ? 
June 7th, 2013, 03:07 AM  #19  
Senior Member Joined: May 2013 Posts: 118 Thanks: 10  Re: A new approach to Fermat's last theorem Quote:
For every prime N of the 6q+1 form,there are exactly N1 non trivial trios of remainders (a,b,c), satisfying the following relations 0<a<N, 0<b<N, 0<c<N and or equavalently: r\:N^2a^Nc^N(ac)^N\r\:N^2b^Nc^N(bc)^N" /> Here's a list for the first 2 such primes for ?=7 the trios (a.b,c) are: (2,4,6), (1,4,5), (1,2,3), (6,5,4), (6,3,2), (5,3,1) for N=13 the trios are3,9,12), (5,6,11), (1,9,10), (2,6,, (2,5,7), (1,3,4), (12,10,9), (12,4,3), (11,8,6), (11,7,5), (10,4,1), (8,7,2) A trio of the form (b,a,c) is trivial to (a,b,c) In half of these N1 trios we have a+b=c and in the other half we have a+b=N+c As the reader can see,we always have: Primes of the 6q1 form don't have trios at all Numbers X=AN+a, Y=BN+b and Z=CN+c don't exist,because you can't find quotients A,B,C to satisfy:  
June 7th, 2013, 03:42 PM  #20  
Senior Member Joined: Sep 2010 Posts: 221 Thanks: 20  Re: A new approach to Fermat's last theorem Quote:
Quote:
Quote:
It is well known and can be easily proved that to have solution the latter requires XYZ to be divisible by N. Then the inverse statement must be true as well: If coprime with then has no solution. It is an equivalent of this elaborated proof, isn't it.  

Tags 
approach, fermat, theorem 
Search tags for this page 
Fermat's last theorem forums in india,a new approach to fermat's last theorem,fermats last theorem short proof 10 pages pdf,Fermat benghli,http://www.mymathforum.com/viewtopic.php?f=40&t=40857 Reply,congurances,Congurance modlo use in exponent,Fermat's last theorem in bengali,case1 fermats little theorem,who is inveted the theorem 6
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fermat last Theorem  mente oscura  Number Theory  10  June 6th, 2013 09:33 PM 
A new approach to Fermat's last theorem  bruno59  Number Theory  0  May 30th, 2013 11:57 AM 
Fermat's Last Theorem  McPogor  Number Theory  15  May 31st, 2011 08:31 AM 
fermat's last theorem????  smslca  Number Theory  4  September 14th, 2010 09:00 PM 
Fermat's last theorem  xfaisalx  Number Theory  2  July 25th, 2010 05:59 AM 