MathDB

The set

\{1, 2, 3, 4\}

can be partitioned into two subsets

A = \{1, 4\}

and

B = \{3, 2\}

with no common elements and such that the sum of the elements of

A

is equal to the sum of the elements of B. Such a partition is impossible for the set

\{1, 2, 3, 4, 5\}

and also for the set

\{1, 2, 3, 4, 5, 6\}

. Determine all values of

n

for which the set of the first

n

natural numbers can be partitioned into two subsets with no common elements such that the sum of the elements of each subset is the same.

1