MathDB

Show that for any finite set

S

of distinct positive integers, we can find a set

T \supseteq S

such that every member of

T

divides the sum of all the members of

T

.
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.

Problem Statement