  The paper is devoted to some applications of Stepanov method. In the first
part of the paper we obtain the estimate of the cardinality of the set, which
is obtained as an intersection of additive shifts of some different subgroups
of F^*_p. In the second part we prove a new upper bound for Heilbronn's
exponential sum and obtain a series of applications of our result to
distribution of Fermat quotients. Also we study additive decompositions of
multiplicative subgroups.
