Consider a rectangle with coordinates $(0,0), (3,0), (3,2),
(0,2)$ and count the number of lattice points (points with whole
number coordinates, coloured yellow in the diagram) on the
perimeter and inside the rectangle.
Define $k$points as points with coordinates $({a\over k},
{b\over k})$ where $a, b$ and $k$ are integers. For example, for
the rectangle in the diagram the yellow points are the lattice
points, $k=1$, and the 2points are the red and yellow points taken
together.
