If I have a set $A$ with positive and negative numbers, and a number to find C.

It is possible to reduce the problem to one with only positive numbers in set $A$?

I mean, it is possible to find a new set $A$ and a new number $C$, so $A$ were only positive numbers, but the same problem?

  • 1
    $\begingroup$ Have you tried to solve this for a particular problem, and then generalise? $\endgroup$ Apr 23 '14 at 16:33
  • $\begingroup$ What have you tried? For us to help you understand, you need to show us in the question what you've tried and where you got stuck, and preferably try to frame a precise question about it. $\endgroup$
    – D.W.
    Apr 24 '14 at 22:32

Hint: Let $A = \{ a_1,\ldots,a_n \}$. Choose a large number $M$ and consider the set $\{ M + a_1, \ldots, M + a_n, M, \ldots, M \}$ ($n$ times the number $M$) and the target $nM + C$. If you want an actual set, instead of taking $n$ times the number $M$, take $M,2M,4M,\ldots,2^{\lceil \log_2 n \rceil}M$ (we assume that $0 \notin A$; otherwise, remove $0$ from $A$).

  • $\begingroup$ Thak you very much :-) $\endgroup$
    – Pedro
    Apr 23 '14 at 18:53

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