Understanding Fermat's Last Theorem: A General Overview

[ahrkron]

Does anyone have a general idea about how the theorem was proven?

The details, of course, are not suitable for posting in the forum. What I'd like to find is the general overview of the theorem from which FLT was obtained as a corollary.

 

[Mr. Robin Parsons]

Respectfully, as one who tried (succeeded?) at this one, all you really need to do is prove is that, for all values of n > 2 the resultant is no longer a right angle triangle.

At least that was how I went about it, some success, but I suspect it isn't a viable as I would have liked it to be as I ended up needing to sort of take a shortcut to arrive at conclusive proof.

 

[KLscilevothma]

http://www.mathforum.org/library/drmath/view/51506.html

 

[selfAdjoint]

The story of the proof, and its connection to the Tamiyama-Shimura conjecture, is told here .

 

[Mr. Robin Parsons]

Originally posted by selfAdjoint
The story of the proof, and its connection to the Tamiyama-Shimura conjecture, is told

Had heard that Mr. Wiles had reduced (the length) his proof using some (easier) algebra...down from the original at 'X' (sorry don't recall right now) hundred pages.

 

[HallsofIvy]

What possible connection could xⁿ+yⁿ= zⁿ for n> 2 have with a right triangle?

And when you say "the resultant is no longer a right angle triangle", what "resultant" are you talking about??

 

[Mr. Robin Parsons]

Originally posted by HallsofIvy
What possible connection could xⁿ+yⁿ= zⁿ for n> 2 have with a right triangle?
And when you say "the resultant is no longer a right angle triangle", what "resultant" are you talking about??

Because at the value of 2 it produces a right angle triangle, Pythagoran (sp?) theorem, and all values greater then 2 (n > 2) will NOT result in a right angle triangle. OK?

 

[HallsofIvy]

I think you MEAN that "if you have a triangle with sides of length a, b, c and such that aⁿ+ bⁿ= cⁿ with n and integer greater than 2, then the triangle is not a right triangle." That's surely true but I don't see what it has to do with Fermat's Last Theorem. For one thing, it says nothing about a, b, c being integers.

 

[Mr. Robin Parsons]

Originally posted by HallsofIvy
I think you MEAN that "if you have a triangle with sides of length a, b, c and such that aⁿ+ bⁿ= cⁿ with n and integer greater than 2, then the triangle is not a right triangle." That's surely true but I don't see what it has to do with Fermat's Last Theorem. For one thing, it says nothing about a, b, c being integers.

No it doesn't, but it is an approach to the problem, none the less.

 

[HallsofIvy]

By the way, to recognize a "church" as a separate entity says nothing about recognizing what it says as true of false- only accepting that it DOES say something. I have a friend who is a professor of religion. She was quick to correct someone who referred to her as a professor of "theology"- her point is that to study something you must believe it exists. To study theology (the study of God) you must believe God exists. To study religion, you only need to believe that religions exist.

 

[Mr. Robin Parsons]

Originally posted by HallsofIvy
By the way, to recognize a "church" as a separate entity says nothing about recognizing what it says as true of false- only accepting that it DOES say something. I have a friend who is a professor of religion. She was quick to correct someone who referred to her as a professor of "theology"- her point is that to study something you must believe it exists. To study theology (the study of God) you must believe God exists. To study religion, you only need to believe that religions exist.

Kinda off topic are we, please, either PM, or start a new thread.