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e \in B, e divides an odd number of elements of B, iff e \in A

Source: Rioplatense 1998 L3 P3

September 19, 2022
number theorydivides

Problem Statement

Let XX be a finite set of positive integers. Prove that for every subset AA of XX, there is a subset BB of XX, with the following property: For each element e e of XX, ee divides an odd number of elements of BB, if and only if ee is an element of AA.
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