Problem 4.  Let $n \ge 2$ be an integer. Initially, the number $1$ is written $n$ times on a blackboard. An operation consists of choosing two numbers $a$ and $b$ currently on the blackboard, not both zero, and replacing them with the numbers \[ \frac{(a - b)^2}{a + b} \quad \text{and} \quad \frac{4ab}{a + b}. \]Determine all integers $n$ for which it is possible, after a finite number of operations, for the number $n$ to appear on the blackboard. Solution 1Solution 1 Solution 2 Solution2 Solution 3 Solution3 Solution 4 Solution4