On a blackboard there are
![n \geq 2, n \in \mathbb{Z}^{+}](/media/m/4/8/3/483a205a00b7c8bb05c314947ea8835b.png)
numbers. In each step we select two numbers from the blackboard and replace both of them by their sum. Determine all numbers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which it is possible to yield
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
identical number after a finite number of steps.
%V0
On a blackboard there are $n \geq 2, n \in \mathbb{Z}^{+}$ numbers. In each step we select two numbers from the blackboard and replace both of them by their sum. Determine all numbers $n$ for which it is possible to yield $n$ identical number after a finite number of steps.