MathDB

Let

n\ge3

be a positive integer. We say that a set

S

of positive integers is good if

|S|=n

, no element of S is a multiple of n, and the sum of all elements of

S

is not a multiple of

n

either. Find, in terms of

n

, the least positive integer

d

for which there exists a good set

S

such that there are exactly d nonempty subsets of

S

the sum of whose elements is a multiple of

n

.
Proposed by Aleksandar Makelov, Burgas, Bulgaria and Nikolai Beluhov, Stara Zagora, Bulgaria

Problem Statement