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Math Help - Sets of integers, different sums

  1. #1
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    Sets of integers, different sums

    There is a natural number . Prove that from any set consisting of integer numbers that has more than elements we can take a subset S that has elements and:
    For any two different subsets the sum of all elements of set is different from the sum of all elements of set . (We assume that the sum of all elements of an empty set equals 0).

    I would be really grateful if anyone could help me with this assignment.

    I've already tried set theory and induction. Now I think this problem must have something to do with number theory, but this branch is so vast that I don't know where to start looking.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    By "no more than 3^k elements", perhaps you mean "at least 3^k elements"? Because for instance if your set contains less than k+1 elements, you certainly can't pick a subset of it having k+1 elements.

    Please check the exact statement of the problem!
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