MathDB
integer coordinates

Source: Ireland 1993

June 29, 2009
analytic geometrymodular arithmeticgeometry unsolvedgeometry

Problem Statement

Show that among any five points P1,...,P5 P_1,...,P_5 with integer coordinates in the plane, there exists at least one pair (Pi,Pj) (P_i,P_j), with i \not\equal{} j such that the segment PiPj P_i P_j contains a point Q Q with integer coordinates other than Pi,Pj P_i, P_j.
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