Question 96
A set $A$ of integers is called sum-full if $A\subseteq A+A$: every element $a\in A$ is the sum of a pair (not necessarily unique) of elements $b,c\in A$ (not necessarily distinct). A set $A$ of integers is called 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?
Does there exist a sum-full zero-sum-free set of integers?