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Spain Mathematical Olympiad
2020 Spain Mathematical Olympiad
3
3
Part of
2020 Spain Mathematical Olympiad
Problems
(1)
Rectangular parallelepiped with all vertices of the same color
Source: Spain Mathematical Olympiad 2020 P3
7/14/2020
To each point of
Z
3
\mathbb{Z}^3
Z
3
we assign one of
p
p
p
colors.Prove that there exists a rectangular parallelepiped with all its vertices in
Z
3
\mathbb{Z}^3
Z
3
and of the same color.
combinatorics
lattice
Spain