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From: eestath on 2 Dec 2009 23:09
i sipmply claim:

for all k>2: p+q=2k if p and q are odd and p/=q!
for all k>1: p+q=2k if p=q!

thus i cover all the cases

can anyone find a k sutch that p+q/=2k
simply NOT

Goldbach conjecture states that every even integer greater then 4 is
the sum of two primes



Proof

Theorem

Golbach conjecture is true for every n>4 if the two prime numbers are
different

Proof
/= (different from)
Suppose that p/=q and that exist a k (positive integer) such that p+q/
=2k then we have:
Is interesting to notice that p and q are odd.

2^(p+q)=2^(2k)=>
2*2^(p/q)/=2^(2k/q)

Theorem 2^(p/q) is irrational number if q does not devide p ( in this
case is allways irrational because p and q are different prime
numbers)

So 2*2(p/q) is irrational

In order 2^(2k/q) to be different from 2*2^(p/q), 2^(2k/q) must be
rational (it cannot be irrational from the assumption)

So k must be devided by q or
k=w*q (w>=1 a positive integer)

We have a contradiction

if k= w*q then we have:

p+q/=2k=>
p/=2k-q=>
p/=2*w*q -q=>
p/=q*(2w-1)

q is odd from the assumption and 2w-1 is odd (the product of odd
numbers is always odd)
So p must be different from odd which contradicts the assumption.
Q.E.D.

If p=q Goldbach conjecture is true.

Thus Goldbach conjecture is true for every number greater or equal to
4
From: David C. Ullrich on 3 Dec 2009 10:46
On Wed, 2 Dec 2009 20:09:10 -0800 (PST), eestath
<stathopoulosee(a)gmail.com> wrote:

>i sipmply claim:

(*)
>for all k>2: p+q=2k if p and q are odd and p/=q!

This is simply nonsense. No matter how many times you
say it. Look:

Let k = 6. Let p = 7. Let q = 11. Then k > 2, k is even,
p and q are odd primes, p is not equal to q.

So (*) implies that 6 = 7 + 11.

Don't tell me to read what you wrote carefully.
People have been doing that. _You_ should read
what everyone else is writing carefully.

>for all k>1: p+q=2k if p=q!
>
>thus i cover all the cases
>
>can anyone find a k sutch that p+q/=2k
>simply NOT
>
>Goldbach conjecture states that every even integer greater then 4 is
>the sum of two primes
>
>
>
>Proof
>
>Theorem
>
>Golbach conjecture is true for every n>4 if the two prime numbers are
>different
>
>Proof
> /= (different from)
>Suppose that p/=q and that exist a k (positive integer) such that p+q/
>=2k then we have:
>Is interesting to notice that p and q are odd.
>
>2^(p+q)=2^(2k)=>
>2*2^(p/q)/=2^(2k/q)
>
>Theorem 2^(p/q) is irrational number if q does not devide p ( in this
>case is allways irrational because p and q are different prime
>numbers)
>
>So 2*2(p/q) is irrational
>
>In order 2^(2k/q) to be different from 2*2^(p/q), 2^(2k/q) must be
>rational (it cannot be irrational from the assumption)
>
>So k must be devided by q or
>k=w*q (w>=1 a positive integer)
>
>We have a contradiction
>
>if k= w*q then we have:
>
>p+q/=2k=>
>p/=2k-q=>
>p/=2*w*q -q=>
>p/=q*(2w-1)
>
>q is odd from the assumption and 2w-1 is odd (the product of odd
>numbers is always odd)
>So p must be different from odd which contradicts the assumption.
>Q.E.D.
>
>If p=q Goldbach conjecture is true.
>
>Thus Goldbach conjecture is true for every number greater or equal to
>4

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
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