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Contest problems with connections to deeper mathematics
IMO 2007 P6. Let $n$ be a positive integer. Consider the set $S$ of points $(x, y, z)$ with $x, y, z \in \{0, 1, \dots, n\}$ and $x + y + z > 0$, so $S$ is a set of $(n+1)^3 - 1$ points in three-dimen …