Let m 2 be an integer. Let A be a finite set of (not necessarily positive) integers, and let B1, …

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Let m gt; 2 be an integer. Let A be a finite set of (not necessarily positive) integers, and let B1, B2, B3, ..., Bm be subsets of A. Assume that for each k = 1, 2, ..., m, the sum of the elements of Bk is mk. Prove that A contains at least m/2 elements.

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