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Lattice points inside a convex body

Source: Romania TST 2 2010, Problem 4

August 25, 2012
geometrycalculusintegrationalgebrafunctiondomainsimilar triangles

Problem Statement

Let nn be an integer number greater than or equal to 22, and let KK be a closed convex set of area greater than or equal to nn, contained in the open square (0,n)×(0,n)(0, n) \times (0, n). Prove that KK contains some point of the integral lattice Z×Z\mathbb{Z} \times \mathbb{Z}.
Marius Cavachi
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