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Am still trying to find a simple solution of FLT. I think I remember that someone proved that if a solution exist to FLT that either x, y or z must have a factor of n. Is this true and, if so, where can I find the proof of this?
I presume you meant [tex] n \in \mathbb{N}\right\backslash\{1,2\}[/tex]Zurtex said:I'm assuming you mean Fermats Last Theorem and not Fermats Little Theorem.
The theorem states that there exits no solution for:
[tex]\left. x^n + y^n = z^n \quad \forall \, x, y, z, n \in \mathbb{N} \right\backslash \{ 1 \}[/tex]
And it has been proven true.
Do you mean this n to be the same as the power in x^{n}+ y^{n}= z^{n}?vantheman said:Yes, I was referring to Fermat's Last Theorem. I know Andrew Wile has already solved it, but there is that remote possibility that Fermat's "truely marvelous proof" does exist.
It may seem like a waste of time to a serious mathematician, but amuse me if you will.
I don't understand your reply because I do not have the mathmetical credentials. Let me re-phrase the question. Prior to Wile's proof, did anyone prove that, in order for a solution to exist, either x, y or z must have a factor of n?
Are you sure of that? The cases n= 3, 4, 5 were quickly proved but the method used did not extend to n larger than 5.I don't feel my efforts have been wasted. I have developed an independent proof for n=3 using simple algebra and congruences. It has been reviewed by the Math Dept of a local university and sent to the College Mathmetical Journal for possible publication.
If the above proof exists, it will go a long way to extending the proof for n=3 to be a proof for all prime values of n. HELP.
You are of course right, doh!HallsofIvy said:I presume you meant [tex]\left. n \in \mathbb{N}\right\backslash\{1,2\}[/tex]
I've never heard of that before. In fact that sounds weird, because the trouble with the methods of proving it for specific cases only struggled on certain prime numbers. I think composite numbers were really easy to deal with, before Wile's proof I think it was something like all n < 10'000'000 were proven.vantheman said:Let me state it again:
Prior to Wile's proof, did anyone prove that in order for a solution to exist to the equation
x^n + y^n = z^n in non-zero integers
that either x, y or z must have a factor of n?
Also, since my proof for n=3 has the possibility, through binomial expansion techniques, to be a tool for proving the equation for all prime values of n, an existing proof of the question I posed will help me in extending my proof for n=3 to n = all prime numbers.
Germain showed this is the case if n and 2n+1 are prime. Actually she proved something a little more general have a look for Sophie Germain's theorem or Sophie Germain primes. I've never seen a full generalization that holds for all primes n.vantheman said:Let me state it again:
Prior to Wile's proof, did anyone prove that in order for a solution to exist to the equation
x^n + y^n = z^n in non-zero integers
that either x, y or z must have a factor of n?
...in a simple waykeebs said:A simple solution for FLT would arise if you could prove the abc conjecture...
WeeDie said:The proof lies in understanding the connection between the prime 2 and 2nd orders of multitude. 2 being the only prime devisable by 2.
I think it would be easier to see the connection using 3 dimensional models with movement in time related to phi - using base 6, as there's only 5 platonic solids in a 3 dimensional universe; 5 dimensional universe if you include time and observer.
I hope this clears things up