Question

prove that for every natural numbers n greater than 2 allways will be (exist) two primes p and q so that this equation n=(p-1)/2 +(q-1)/2 +1 is true .

Answer 1

for example : 3=(3-1)/2 +(3-1)/2 +1
3=2/2 +2/2 +1
3=1+1+1
3=3

Answer 2

I think this is related to Goldbach's conjecture that every even integer is the sum of two primes.
http://en.wikipedia.org/wiki/Goldbach%27s_conjecture
Since if
\[
n = \frac {p-1} 2+ \frac {q-1}2 +1 \\
2 n = p-1 + q-1 +2 =p+q
\]

Answer 3

- so because every prims can be writing in the form of p=2x+1 and q=2y+1
where x and y are natural numbers so than :
2x+1-1 2y+1-1
n=-------- + -------- +1
2 2

n= 2x/2 +2y/2 +1

n=x+y+1 - so what can proving verx easy by induction that is true

Answer 4

very easy - sorry

Answer 5

There is something wrong in your writing above, or I misunderstood your question. Your question and I am copying and pasting is
"prove that for every natural numbers n greater than 2 allways will be (exist) two primes p and q so that this equation n=(p-1)/2 +(q-1)/2 +1 is true .
"
In your proof, you defined n the way you want to be, but the question was to prove that
every n can be written as
n=(p-1)/2 +(q-1)/2 +1
If you prove this, you would be very famous!!!

You have to construct p and q from n and not vice versa.

Answer 6

- ok i understand it but you need to know again that n is an indifferent natural number greater than 2
- secondly by definition every primes greater than 2 can be writing in the form of
2n+1 ,where n is a natural number
- 3. - by induction is very easy proving that every n ,natural numbers grater than 2 ,can be writing like a sum of two natural numbers x and y plus 1 , so like n=x+y+1,
- 4. - so than p=2x+1 and q=2y+1 ,where p and q are primes grater than 2 and x,y are natural numbers ,so than the statement

n = (p-1)/2 +(q-1)/2 +1

can be writing like

n=(2x+1-1)/2 +(2y+1-1)/2 +1
n=2x/2 +2y/2 +1
n=x+y+1

Answer 7

I said what I said before, It does not seem that you get it.
Sorry.