A lattice point is a point (x, y) in the plane, both of whose coordinates are integers.
It is easy to see that every lattice point can be surrounded by a small circle which
excludes all other lattice points from its interior. It is not much harder to see that
it is possible to draw a circle which has exactly two lattice points in its interior, or
exactly 3, or exactly 4. Do you think that for every positive integer n there is a circle in the plane which contains exactly n lattice points in its interior? Justify your answer.
