# 2013-12 Equilateral triangle in R^n

Let $$A = \{ (a_1, a_2, \cdots, a_n : a_i = \pm 1 \, (i = 1, 2, \cdots, n) \} \subset \mathbb{R}^n$$. Prove that, for any $$X \subset A$$ with $$|X| > 2^{n+1}/n$$, there exist three distinct points in $$X$$ that are the vertices of an equilateral triangle.

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