Very very bored...
Now for some maths lesson.
Fermat's Last Theorem states that
x^n + y^n = z^n
has no non-zero integer solutions for x, y and z when n > 2.
Ok so this is a theorem, actually not proven by him, because he basically proved it wrongly. Therefore he is sort of the creator of this problem. Yeah so basically this was proven in 1994, and of course i'm not gonna copy paste the whole thing down, because the proof is about 100 odd pages.
Right so now i don't know what the hell i'm reading. Basically its the combination of 2 theorem.
First is about the elliptic curve by Frey(not Sebastian Frey) which goes like this:
y^2 = x(x-a^n)(x+a^n)
After some, or rather many calculations, they showed that it is not modular.
Therefore this leads to the 2nd form of concept by a french i believed, Jean-Pierre Serre - The Taniyama-Shimura conjucture, don't ask me how this came about, nice name though.
Taniyama-Shimura conjucture states that if the Galois representation associated with an elliptic curve E has certain properties, then E cannot be modular. Specifically, it cannot be modular in the sense that there exists a modular form which gives rise to the same Galois representation.
Let S(N) be the (vector) space of cusp forms....(OMFG vector space!!!Now truly lost in space.)
So after the concept is applied, together fusing with other equations and concepts together, you get...
It can be shown that if f(z) is a cusp form which is a normalized eigenfunction for all T(p), then there is an Euler product decomposition for the L-function L(f,s). This is obviously of great technical usefulness in relating L-functions of forms and those of elliptic curves (which are Euler products by definition).
I believed after doing all this shit, they just proved that E is not modular.
But the Frey curve is semistable, so the semistable case of the Taniyama-Shimura conjecture, which Wiles proved, implies the curve is modular. This contradiction means that the assumption of the existence of a nontrivial solution of the Fermat equation must be wrong, and so FLT is proved.
I think this about sums it up, just that after this they still had to proof the semistable case of Taniyama-Shimura Conjucture.
LOL, what a way to waste some time...
PS. info provided by http://cgd.best.vwh.net/home/flt/flt08.htm
Fermat's Last Theorem states that
x^n + y^n = z^n
has no non-zero integer solutions for x, y and z when n > 2.
Ok so this is a theorem, actually not proven by him, because he basically proved it wrongly. Therefore he is sort of the creator of this problem. Yeah so basically this was proven in 1994, and of course i'm not gonna copy paste the whole thing down, because the proof is about 100 odd pages.
Right so now i don't know what the hell i'm reading. Basically its the combination of 2 theorem.
First is about the elliptic curve by Frey(not Sebastian Frey) which goes like this:
y^2 = x(x-a^n)(x+a^n)
After some, or rather many calculations, they showed that it is not modular.
Therefore this leads to the 2nd form of concept by a french i believed, Jean-Pierre Serre - The Taniyama-Shimura conjucture, don't ask me how this came about, nice name though.
Taniyama-Shimura conjucture states that if the Galois representation associated with an elliptic curve E has certain properties, then E cannot be modular. Specifically, it cannot be modular in the sense that there exists a modular form which gives rise to the same Galois representation.
Let S(N) be the (vector) space of cusp forms....(OMFG vector space!!!Now truly lost in space.)
So after the concept is applied, together fusing with other equations and concepts together, you get...
It can be shown that if f(z) is a cusp form which is a normalized eigenfunction for all T(p), then there is an Euler product decomposition for the L-function L(f,s). This is obviously of great technical usefulness in relating L-functions of forms and those of elliptic curves (which are Euler products by definition).
I believed after doing all this shit, they just proved that E is not modular.
But the Frey curve is semistable, so the semistable case of the Taniyama-Shimura conjecture, which Wiles proved, implies the curve is modular. This contradiction means that the assumption of the existence of a nontrivial solution of the Fermat equation must be wrong, and so FLT is proved.
I think this about sums it up, just that after this they still had to proof the semistable case of Taniyama-Shimura Conjucture.
LOL, what a way to waste some time...
PS. info provided by http://cgd.best.vwh.net/home/flt/flt08.htm
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