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2003 BAMO p3 lattice points, 3 point of triangle with integer area

Source:

August 26, 2019

lattice pointsgeometrycombinatorial geometryIntegerareas

Problem Statement

A lattice point is a point

(x, y)

with both

x

and

y

integers. Find, with proof, the smallest

n

such that every set of

n

lattice points contains three points that are the vertices of a triangle with integer area. (The triangle may be degenerate, in other words, the three points may lie on a straight line and hence form a triangle with area zero.)

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