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[move to other probs plz] Points

Source: flanders '03

August 9, 2004
analytic geometryparameterizationnumber theoryleast common multipleratiocalculusintegration

Problem Statement

Consider all points with integer coordinates in the carthesian plane. If one draws a circle with M(0,0) and a well-chose radius r, the circles goes through some of those points. (like circle with r=22r=2\sqrt2 goes through 4 points) Prove that ∀n∈N,∃r\forall n\in \mathbb{N}, \exists r so that the circle with midpoint 0,0 and radius rr goes through at least nn points.
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