Re: Fermat's last theorem and a counter example

In article <216678.1141659400143.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
bassam king karzeddin <bassam@xxxxxxxxxx> wrote:
In article
<7432441.1141645390092.JavaMail.jakarta@xxxxxxxxxxxxxx
orum.org>,
bassam king karzeddin <bassam@xxxxxxxxxx> wrote:
Dear All

FLM states simply that the following equation:

x^n + y^n = z^n

Doesn't have solution in the whole positive integer
number system for (x, y, z, n), where (n>2)

Iff, exists a counter example to FLM, then the
following conditions must obey:

All odd prime factors of (x+y) must be some prime
factors of (z)

All odd prime factors of (z-x) must be some prime
factors of (y)

All odd prime factors of (z-y) must be some prime
factors of (x)

gcd(x,y)=1

2*z > x+y > z

(z-y)>2

z>y>x

The example you were given already satisfies all of
these conditions:

x=35, y=46, z=51

The only odd prime factor of x+y=81 is 3, which
divides z.
There are no odd prime factors of z-x=16, so they all
divide y.

That is my point

Then you should phrase your statement differently. ALL odd prime
factors of z-y divide x. This SATISFIES the condition you stated. If
you meant something else, then you should have written something else.


If,doesn't exist odd prime factor for (z-x) or (z-y), then it is not
a counter example,

No. If there are no odd prime factors for z-x, then z-x satisfies the
condition vacuously. If you want to exclude the possibility of z-x,
z-y, or x+y being a power of 2, then you need to say so EXPLICITLY; it
is NOT included in saying "all odd prime factors satisfy X", because
any power of 2 satisfies such a condition vacuously.

Note that when I say "All odd prime factors of (z-x) are also prime factors of (y)"

But where are the odd prime factors of (16)

Please show me an odd prime factor of 16 that does NOT divide y. Then
you'll have a point.

I mean actually (z-x) must have at least one odd prime factor that is
also a prime factor of (y),

That may very well have been what you meant. Alas for you, it was most
decidedly NOT what you said.


--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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