For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there exists a circle of area n which contains exactly n lattice points in its interior. Schinzel's theorem shows that for every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference.

circle | circle point picking | circumference | Gauss's circle problem | Kulikowski's theorem | lattice point | Schinzel circle | Schinzel's theorem