lattice point is a point $(x,y)$ in the plane, both of whose coordinates are integers. It is easy o see that every lattice point can be surrounded by a small circle which excludes all other attice points from its interior. It is not much harder to see that it is possible to draw a circle vich has exactly two lattice points in its interior, or exactly $3,$ or exactly $4,$ as shown in the icture below.

Oo you think that for every positive integer $n$ there is a circle in the plane which contains xactly $n$ lattice points in its interior? Justify your answer.