Earlier results by Alon, Lipkin, and Alon--Freiman utilized
the analytic circle method. Our proof is completely elementary,
apart from the application of a generalization of the Erd\H os--Heilbronn
conjecture that was proved recently by Dias da Silva--Hamidoune,
and also by Alon--Nathanson--Ruzsa, using algebraic tools.
Our first result, combined with other combinatorial ideas, allows
us to confirm the following conjecture of Lev. Let
$1\le a_1<\ldots
Document last modified on April 12, 1996