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maximum possible number of points with integer coordinates

Source: Iran Third Round MO 1998, Exam 2, P3

October 31, 2010
analytic geometrygeometry unsolvedgeometry

Problem Statement

Let n(r)n(r) be the maximum possible number of points with integer coordinates on a circle with radius rr in Cartesian plane. Prove that n(r)<63πr23.n(r) < 6\sqrt[3]{3 \pi r^2}.
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