Re: Fermat's Last theorem short proof
- From: quasi <quasi@xxxxxxxx>
- Date: Mon, 23 Apr 2007 19:57:30 -0500
On Mon, 23 Apr 2007 23:27:25 GMT, V <V@xxxxxxxxxx> wrote:
gcd (x+y, (x^n+y^n)/(x+y)) = gcd (x+y, n) if x and y are coprime and n
is odd and > 1.
x^n+y^n = gcd(x+y,n)^2 * (x+y)/gcd(x+y,n) * ((x^n+y^n)/(x+y))/gcd(x+y,n)
x^n+y^n is divisible by (x+y) and gcd(x+y,((x^n+y^n)/(x+y))/gcd(x+y,n))=1
For c^n to be a solution, c needs to be a multiple of (x+y),
The error is right here (the above line).
None of your above analysis concerning common factors justifies your
claim that c is a multiple of x+y. All you know is that c^n is a
multiple of x+y.
Let's take the easy case where x+y and (x^n+y^n)/(x+y) have no common
factor. Letting a=x+y and b=(x^n+y^n)/(x+y), you have
c^n=ab where a,b are coprime.
That does not imply that c is a multiple of a (unless a is prime).
So your proof fails.
quasi
.
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