On an extremal problem in number theory (Q1393437)

Let \(h(n)\) be the largest function of \(n\) such that, from any set of \(n\) nonzero integers, one can always extract a subset of \(h(n)\) integers with the property that any two sums formed from its elements are equal only if they have equal number of summands. The aim of this paper to obtain the result \[ h(n) \gg n^{1/3}(\log n)^{1/3} \] which is a refinement over a previous estimate of Erdős, namely \(h(n) \gg n^{1/3}\).