MathDB

4

Part of 2019 China Girls Math Olympiad

Problems(1)

Chinese Girls Mathematical Olympiad 2019, Problem 4

Source:

8/12/2019
Given parallelogram OABCOABC in the coodinate with OO the origin and A,B,CA,B,C be lattice points. Prove that for all lattice point PP in the internal or boundary of △ABC\triangle ABC, there exists lattice points Q,RQ,R(can be the same) in the internal or boundary of △OAC\triangle OAC with OP→=OQ→+OR→\overrightarrow{OP}=\overrightarrow{OQ}+\overrightarrow{OR}.
combinatoricslattice pointsgeometryvectorparallelogram