Can anyone tell whether my proof is correct?
Let x and y be two non-prime odd numbers and z be any even number.
Now,
every even number can be expressed as the sum of two odd numbers,
Therefore,
x+y=z
Let k be the common factor of x and y.
k is odd _(since x and y are odd)
Therefore,
k(x'+y')=z
=> x'+ y'= m _( since k is a factor of z)
m is even _(since even÷odd=even)
Now x' and y' are prime numbers and m is even.
Hence, every even number can be expressed as the sum of two prime numbers.
Let x and y be two non-prime odd numbers and z be any even number.
Now,
every even number can be expressed as the sum of two odd numbers,
Therefore,
x+y=z
Let k be the common factor of x and y.
k is odd _(since x and y are odd)
Therefore,
k(x'+y')=z
=> x'+ y'= m _( since k is a factor of z)
m is even _(since even÷odd=even)
Now x' and y' are prime numbers and m is even.
Hence, every even number can be expressed as the sum of two prime numbers.