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I would like to see a solution to the following problem:

Let A be a finite collection of natural numbers. Consider the set of the pairwise sums of each of the numbers in A, which I will denote by S(A). For example, if A={2,3,4}, then S(A)={5,6,7}. Prove that if S(A)=S(B) for two different finite sets of natural numbers A and B, then |A|=|B|, and |A|=|B| is a power of 2.

I find this problem interesting, but I am working on other problems. Anyone have ideas?

Thanks,

Mathguy

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# Combinatorial Number Theory Problem

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