Problem of the Week

The figure below shows circles in the plane which contain exactly one, two, three, four, and five lattice points in their interior.  (A lattice point has both of its coordinates being integers.)

Either:

(a)  Show that for each positive integer n there is a way to draw a circle in the plane which will contain exactly n lattice points in its interior, or

(b)  Find the smallest positive integer n for which it is impossible to draw a circle in the plane which contains exactly n lattice points in its interior.  Explain conclusively that your answer is mininal.

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©2001 Alberto L Delgado