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## Two-distance sets

Let \(d_1, d_2 \in \mathbb{R}\), and let \(S \subset \mathbb{R}^n\) be a set of vectors such that \(|| x - y || \in \){\(d_1, d_2\)} for all \(x, y \in S\).

Prove that there exists such a set \(S\) of size \({n \choose 2}\).

Prove that every such set \(S\) has at most \(\frac{1}{2}(n+1)(n+4)\) points.