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Subset in the coordinate plane - ILL 1990 KOR3

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September 19, 2010
analytic geometrygeometryparallelogramvectorgeometric transformationhomothetyratio

Problem Statement

Let LL be a subset in the coordinate plane defined by L={(41x+2y,59x+15y)∣x,y∈Z}L = \{(41x + 2y, 59x + 15y) | x, y \in \mathbb Z \}, where Z\mathbb Z is set of integers. Prove that for any parallelogram with center in the origin of coordinate and area 19901990, there exist at least two points of LL located in it.
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