Question 9
Let $n$ and $k$ be positive integers. There are given $n$ circles in the plane. Every two of them intersect at two distinct points, and all points of intersection they determine are distinct. Each intersection point must be colored with one of $n$ distinct colors so that each color is used at least once, and exactly $k$ distinct colors occur on each circle. Find all values of $n \geq 2$ and $k$ for which such a coloring is possible.