Elegant Proof for Fermat's Last Theorem? (1 Viewer)

[hyparzero]

Fermat's last theorem was proved by Wiles by first prooving the shimura-taniyama conjecture, however, the final proof was more than 150pages, and it was claimed Fermat had a much more elegant ptoof to his theorem, which stated there are no positive integers which satisfy the following condition if n>2

xⁿ + yⁿ = zⁿ

If one has such an elegant proof, how does one submit it for evaluation.

 

[Dumsum]

By posting it here. Maths nerds all around the world patrol this forum. True story.

 

[hyparzero]

and let everyone else steal it? I mean mathematical instituitions.

 

[Templar]

You can post or submit it to any mathematical institute, such as an university. However, that's largely irrelevant as I doubt you will come up with a much simpler proof to the scale of the one Fermat possibly used.

Fermat's Last Theorem was proved using a specialised case of Shimura Taniyama conjecture. The entire conjecture was proved later by Taylor et al, with Taylor the one who helped Wiles patch up his proof.

 

[hyparzero]

Hmmm... i played with the theorem a bit, and what i've done is:

I took on the assumption that the solutions x,y,z to be integers > 0

Then I proved that the ratio of (x,y,z) to one another are always irrational for n>2

Thus, if the ratios are irrational, then (x,y,z) cannot be integers, and hence, there are no integer solutions to the condition:

xⁿ + yⁿ = zⁿ

which proves Fermat's Last Theorem.

Does anyone see a flaw with my reasoning without me going into the details of the proof.

 

[SeDaTeD]

If you have indeed proved that the ratios are irrational, then it seems fair enough to me. If it is true, I'd be surprised if nobody has ever come up with your method before. Try to see if you've missed anything or if there are any flaws. If you are sure there are none, then congratulations .

 

[STx]

heres one i found: http://www.economics.ox.ac.uk/Members/giuseppe.mazzarino/Fermat_March_2003.pdf

 

[Templar]

Partial cases of Fermat's Last Theorem has been proved by reductio ad absurdum, but it's highly unlikely the entirety could be proved as such.

 

[Templar]

What I meant was assuming that x, y and z are integers and then proving there will always be a smaller set, as opposed to the induction used to prove modular curves.

 

[hello2004]

I think I found a very large error in your solution:

Then I proved that the ratio of (x,y,z) to one another are always irrational for n>2

Consider the equation:

x^3 + y^3 = z^3

and let a particular solution be:

x = squareroot(2)
y = squareroot(2)
z = 2^(5/6)

... the ratio of x to y is '1' and is obviously not irrational. I think your solution is invalid as x and y can be linearly related by an infinite amount of constants to which a value 'z' will exist.

 

[hyparzero]

I think I found a very large error in your solution:



Consider the equation:

x^3 + y^3 = z^3

and let a particular solution be:

x = squareroot(2)
y = squareroot(2)
z = 2^(5/6)

... the ratio of x to y is '1' and is obviously not irrational. I think your solution is invalid as x and y can be linearly related by an infinite amount of constants to which a value 'z' will exist.

But the ratio of x to z clearly is.
I proved that all you needed is one ratio to be irrational for all solutions (x,y,z) to be irrational.

The original theorem states no integer solutions exists for (x,y,z), such that for any irrational solution of either x,y or z, the theorem is deemed true.