2009 USAMO 第 2 题

Let $n$ be a positive integer. Determine the size of the largest subset of $\{ - n, - n + 1, \ldots , n - 1, n\}$ which does not contain three elements $a, b, c$ (not necessarily distinct) satisfying $a + b + c = 0$.

令 $n$ 为正整数。确定 $\{ - n, - n + 1, \ldots , n - 1, n\}$ 的最大子集的大小，该子集不包含满足 $a + b + c = 0$ 的三个元素 $a, b, c$ (不一定不同)。