Let n be a positive integer. A finite set of integers is called n-divided if there are exactly n ways to partition this set into two subsets with equal sums. For example, the set {1,3,4,5,6,7} is 2-divided because the only ways to partition it into two subsets with equal sums is by dividing it into {1,3,4,5} and {6,7}, or {1,5,7}
and {3,4,6}. Find all the integers n>0 for which there exists a n-divided set.Proposed by Martin Rakovsky, France JuniorBalkanshortlist2021algebrapartitioning