## A Conversation for The Euler Equation

### Fermat

x25 Started conversation Jun 30, 2000

As a request, could you just put up something on Fermat's last theorem

### Fermat

Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) Posted Jun 30, 2000

Errm... ok. As long as you don't want more than a very rough outline of the proof. It's 150 pages long so it is a bit much for someone to understand

I will post a link here afterwards.

Can I ask what it is you want to know?

### Fermat

x25 Posted Jun 30, 2000

Well, it's like this, if i am not wrong you are talking about the three colour theorem. I am very unsure about this topic and the problem it actually tries to address. Interested in a very rough sketch of the problem and the way the solution approached it (if such a gross simplification is possible). would be very happy with a link that gives a comprehensive view and starts pretty low. This (as you will probably appreciate) is very difficult to obtain on a conventional search engine without a guide. My interest in the problem stems from previous education and an acquaitance.

regards...

### Fermat

26199 Posted Jun 30, 2000

I might be getting horribly confused here, but isn't it a four colour theorem? The one which says, basically, that you can colour in any map with four colours so that no same-colour countries touch...

Either way, I'm fairly sure it's got very little to do with Fermat. Fermat's last theorem says that:

a^n + b^n <> c^n where a, b, c are integers greater than 0 and n > 2.

Sorry, using computer notation there: ^ means 'to the power of', and <> means 'does not equal'.

As for how you prove it, I have absolutely no idea

26199

### Fermat

Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) Posted Jun 30, 2000

The proof for FLT is quite simple. If you re-arrange the FLT equation, you can obtain an elliptic curve. Ken Ribet (I think) proved Frey's argument that this function (a semi-stable elliptic curve) cannot be modular if it is possible. Thus, by proving Taniyama-Shimura for this set of elliptic curves, you prove FLT.

And it is the 4 colour theorum and that proof required amazing amounts of number crunching on computer.

### Fermat

Jim diGriz Posted Jul 1, 2000

Have you read Donald Knuth's fascinating series _The Art of Computer Programming_?

At the start of each book, he has a set of Notes on the Exercises, just to get you used to the kind of difficulty of problems in the text.

Problem 4 right at the beginning of the first volume is:

4. Prove that when n is an integer, n > 2, the equation x^n + y^n = z^n has no solution in positive integers x,y,z.

What a mean man! I mean he doesn't even say that he's asking for a proof of Fermat's Last Theorem!

Just the kind of thing you'd need to tackle in the introduction before you even start the book!

### Fermat

Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) Posted Jul 1, 2000

Oh God... there is a name given to twisted people like that. It's "mathematician"

Not that I can complain

Key: Complain about this post

### Fermat

- 1: x25 (Jun 30, 2000)
- 2: Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) (Jun 30, 2000)
- 3: x25 (Jun 30, 2000)
- 4: 26199 (Jun 30, 2000)
- 5: Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) (Jun 30, 2000)
- 6: Jim diGriz (Jul 1, 2000)
- 7: Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) (Jul 1, 2000)

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