need help from math gurus...purely abstract stuff

[Semidevil]

I'm trying to write a paper on Fermat's Last theorem, and browsing through the web, I found these 2 theorems:

1. If there is a solution(x, y, z, n) to Fermat's theorem, then the elliptic curve defined by the equation
Y^2 = X(x - x^n)(X + Y^n) is semistable but not modular

2. All Semistable elliptic curves w/ rational cofficients are modular.

My resources from the net gives proofs to the 2 theorems, thereby proving the Fermat problem. but I am having trouble relating the theorems to the Fermat problem. what does it mean for an elliptic curve to be semistable and modualar? I just don't see how it relates.

 

[Zim Hosein]

It's all Greek to me Semidevil

 

[TerryMathews]

Multiply both sides of equation by 0. Problem solved.

 

[schizoid]

Originally posted by: Semidevil
I'm trying to write a paper on Fermat's Last theorem, and browsing through the web, I found these 2 theorems:

1. If there is a solution(x, y, z, n) to Fermat's theorem, then the elliptic curve defined by the equation
Y^2 = X(x - x^n)(X + Y^n) is semistable but not modular

2. All Semistable elliptic curves w/ rational cofficients are modular.

My resources from the net gives proofs to the 2 theorems, thereby proving the Fermat problem. but I am having trouble relating the theorems to the Fermat problem. what does it mean for an elliptic curve to be semistable and modualar? I just don't see how it relates.

Perhaps you'd like this joke I just made up...

Q: How do mathemeticians ask out girls?

A: They ask for their Godel numbers. =]

Heh. Honestly, I don't know much about Fermat's last theorem. I do, however, have a proof for the Reiman hypothesis sketched in the margins of a copy of Dos for Dummies, but there isn't enough room for me to finish it!

BTW: Nice to know there's another halfway smart person here on ATOT.

 

[cchen]

a simple search on google will give you a plethora of results
also try searching for andrew wiles

 

[Muzzan]

I haven't got the slightest clue what semistable or modular is either... But I have read Simon Singh's book on the subject *cough*. Basically:

1) All semistable elliptic curves are modular.

2) Any counterexample to Fermat's last theorem gives rise to an elliptic curve which is semistable but not modular. A contradiction to the previous theorem, hence no counterexamples to Fermat's last theorem can exist.

That's how they relate to each other. Or something.

 

[agnitrate]

Originally posted by: cchen
a simple search on google will give you a plethora of results
also try searching for andrew wiles

Yeah, just find what Wiles wrote and how Taylor fixed it. Proof done.

-silver