MathDB

A set

A

of integers is called sum-full if

A \subseteq A + A

, i.e. each element

a \in A

is the sum of some pair of (not necessarily different) elements

b,c \in A

. A set

A

of integers is said to be zero-sum-free if

0

is the only integer that cannot be expressed as the sum of the elements of a finite nonempty subset of

A

. Does there exist a sum-full zero-sum-free set of integers?
Romania (Dan Schwarz)

Problem Statement