Subset sums in $\BZ_p$
  Let $\BZ_p$ be the finite field of prime order $p$ and $A$ be a subset of $\BZ_p$. We prove several sharp results about the following two basic questions:   (1) When can one represent zero as a sum of distinct elements of $A$ ?   (2) When can one represent every element of $\BZ_p$ as a sum of distinct elements of $A$ ? 
H. H. Nguyen, E. Szemeredi and V. H. Vu