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Part of 2002 Taiwan National Olympiad

Problems(1)

lattice point visible from the origin

Source: 11-th Taiwanese Mathematical Olympiad 2002

1/23/2007
A lattice point XX in the plane is said to be visible from the origin OO if the line segment OXOX does not contain any other lattice points. Show that for any positive integer nn, there is square ABCDABCD of area n2n^{2} such that none of the lattice points inside the square is visible from the origin.
geometrycombinatorics unsolvedcombinatorics