Someone wrote: Any integer number divisible by integer k can be represented as the sum of k prime numbers.
This is simply stating in the trivial case for P prime : k.P=P+P+P+...+P, k sums of the same prime.
If P in above sum is not prime, it can be broken up into its prime factors and you get a sum of primes again.
So the above statement is basically the same as the breakup of a number into its prime factors and has not to do with the Goldbach conjecture.

Someone wrote: Any integer number divisible by integer k can be represented as the sum of k prime numbers.

This is simply stating in the trivial case for P prime : k.P=P+P+P+...+P, k sums of the same prime.

If P in above sum is not prime, it can be broken up into its prime factors and you get a sum of primes again.

So the above statement is basically the same as the breakup of a number into its prime factors and has not to do with the Goldbach conjecture.