Fermat's Enigma

[Freeman]

[math]x^n+y^n=z^n[/math] This is fermat's enigma, where n>2. However, [math]\sqrt3^4+2^4=\sqrt5^4[/math] is true. Huh???

[NSX]

http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html

 

Fermat's Last Theorem states that

 

xⁿ + yⁿ = zⁿ

 

has no non-zero integer solutions for x, y and z when n > 2

 

What you did there is just the pythagorean triple of 3, 4 & 5

[Freeman]

Wow, thanks for addressing my question

[jordan]

The link he posted did state that x, y and z had to be non-zero integers.

[Freeman]

No, I am pissed off that I was wrong...

[JaKiri]

It's not Fermat's Enigma, it's Fermat's Last Theorem, which was solved (proved) a decade ago by Andrew Wiles.

[bloodhound]

with someone called Taylor, but most of the credit goes to Wiles. wasn't he from england?

[JaKiri]

with someone called Taylor, but most of the credit goes to Wiles. wasn't he from england?

 

He was from England, and Taylor only helped Wiles in fixing one minor flaw in the proof. Almost all of it was Wiles.

[bloodhound]

u talk of "fixing one minor flaw" as such a small thing. thats what makes or breaks a proof.

[JaKiri]

u talk of "fixing one minor flaw" as such a small thing. thats what makes or breaks a proof.

 

It is a small thing.

 

Insignificant it is not, but the amount of work required was miniscule compared to that Wiles put in.

[bloodhound]

It is still an important piece of work. I 'm sure Wiles could have fixed the flaw himself.

[Primarygun]

Not integer accepted?

[Primarygun]

Wiles was very poor, he needs to think himself wothout revealing this secret to other person for over many years

[bloodhound]

in fact , if u ever bother to read the book called appropriately "Fermat's Last theorem" dont know who its by, it says that wiles isolated himself for several years from the outside world. devoting his time to the proof.

[JaKiri]

in fact , if u ever bother to read the book called appropriately "Fermat's Last theorem" dont know who its by, it says that wiles isolated himself for several years from the outside world. devoting his time to the proof.

 

Well, sort of. He just worked on his own for 7 years on campus. He didn't go and live in the hills or anything similar.

[bloodhound]

hehe. well obviously he not going to do that.

 

anyway back to the topic. the equation in discussion is one example of Diophantine equations. Diophantine equations are just equations in one or more variables for which integer solutions are sought.

 

one other example

 

let p be a prime. Then [math]p=x^2+y^2[/math] has a solution with [math]x,y \in \mathbb{Z}[/math] if and only if p = 2 or p is equivalent to 1 (mod4) [saw this in lecture notes for number theory]