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Math Help - Unique sum for all natural numbers

  1. #1
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    Unique sum for all natural numbers

    I am looking for two infinite subsets of the natural numbers ( A, B \subseteqq N), that any n natural numbers can be written in a unique way as a sum of an elemenet from each sets: n=a+b (where a \in A, b \in B.
    Any help would be appreciated!
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  2. #2
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    Quote Originally Posted by doug View Post
    I am looking for two infinite subsets of the natural numbers ( A, B \subseteqq N), that any n (natural number) can be written in a unique way as a sum of an element from each sets: n=a+b (where a \in A, b \in B).
    You could for example take A to be the set of all natural numbers whose decimal expression has a 0 in all the even-numbered places (counting from the right), and B to be the set of all natural numbers whose decimal expression has a 0 in all the odd-numbered places.

    So for example the number n = 31416265 can be written 1010205 + 30406060 (with the first of those numbers being in A and the second one being in B).
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