MathDB

Let

n \geq 2

be a positive integer. A subset of positive integers

S

is said to be comprehensive if for every integer

0 \leq x < n

, there is a subset of

S

whose sum has remainder

x

when divided by

n

. Note that the empty set has sum 0. Show that if a set

S

is comprehensive, then there is some (not necessarily proper) subset of

S

with at most

n-1

elements which is also comprehensive.

Problem Statement