Erdős-Heilbronn conjecture

Let $A\subset {\mathbb{Z}}_p$ be a set of residues modulo $p$, and let $h$ be a positive integer, then

$$h^{\wedge }A=\{a_1+a_2+\mathrm{\cdots }+a_h\mid a_1,a_2,\mathrm{\dots },a_h\text{ are distinct elements of }A\}$$

has cardinality at least $\min (p,hk-h^2+1)$. This was conjectured by Erdős and Heilbronn in 1964[1]. The first proof was given by Dias da Silva and Hamidoune in 1994.