Let $h(n)$ be maximal such that if $A\subseteq \mathbb{Z}$ with $\lvert A\rvert=n$ then there is $B\subseteq A$ with $\lvert B\rvert \geq h(n)$ such that if $a_1+\cdots+a_r=b_1+\cdots+b_s$ with $a_i,b_i\in B$ then $r=s$.
Straus [St66] proved $h(n) \ll n^{1/2}$. Erdős noted the bound $h(n)\gg n^{1/3}$ and claimed that Choi had proved $h(n) \gg (n\log n)^{1/3}$, although I cannot find such a paper.
