Restricted set addition: The exceptional case of the Erdős–Heilbronn conjecture

Let A≠B be nonempty subsets of the group of integers modulo a prime p. If p⩾|A|+|B|−2, then at least |A|+|B|−2 different residue classes can be represented as a+b, where a∈A, b∈B and a≠b. This result complements the solution of a problem of Erdős and Heilbronn obtained by Alon, Nathanson, and Ruzsa.