Školjka IMO Shortlist 1993 problem N3
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Show that for any finite set 
of distinct positive integers, we can find a set 
⊇ such that every member of divides the sum of all the members of .
Original Statement:
A finite set of (distinct) positive integers is called a DS-set if each of the integers divides the sum of them all. Prove that every finite set of positive integers is a subset of some DS-set.
of distinct positive integers, we can find a set ⊇ such that every member of divides the sum of all the members of . Original Statement:
A finite set of (distinct) positive integers is called a DS-set if each of the integers divides the sum of them all. Prove that every finite set of positive integers is a subset of some DS-set.
Source: Međunarodna matematička olimpijada, shortlist 1993