MathDB

74

Part of 1990 IMO Longlists

Problems(1)

Subset in the coordinate plane - ILL 1990 KOR3

Source:

9/19/2010
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.
analytic geometrygeometryparallelogramvectorgeometric transformationhomothetyratio