MathDB

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\}

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

Problem Statement