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Let n,k \in \mathbb{Z}^{+} with k \leq n and let S be a set containing n distinct real numbers. Let T be a set of all real numbers of the form x_1 + x_2 + \ldots + x_k where x_1, x_2, \ldots, x_k are distinct elements of S. Prove that T contains at least k(n-k)+1 distinct elements.

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