Determine all natural numbers $n$ with $n>1$ that applies: If each grid point of a quadratic grid in the plane is colored with one of n given Colors, then there are always three grid points of the same color, that form a orthogonal triangle form whose catheters are parallel to the grid lines. It is a Cartesian coordinate system.
So I tried to find a solution to this question with Ramsey theory, but so far with no success.