Question 188
Any integer from the set $A = \{1, 2, \dots, 2015\}$ is colored either red or green. For given positive integers $a$ and $b$ we are allowed to change the color of any $a$ or $b$ consecutive integers from $A$. A pair $(a, b)$ is called *good* if it is possible to change the color of all numbers after finite number of moves. A positive integer $t \le 2015$ is called *nice* if all pairs $(a, b)$, for which $a + b = t$ are good. Find all nice numbers.