Igor Shparlinski<br>
speaks on 
"Catalan  and Ap{\'e}ry Numbers in Residue Classes"
(joint work with Moubariz Garaev and Florian Luca)

We estimate character sums with Catalan numbers and middle
binomial coefficients modulo a prime p.  We use this bound
to show that the first at most p^{13/2} (log p)^6
elements of each sequence already fall in all
residue classes modulo every sufficiently large p, which improves
the previously known result requiring p^{O(p)} elements.
 We also study, using a different technique, similar
questions for sequences satisfying polynomial recurrence relations,
for example, for Apery numbers. We show
that such sequences form a finite additive basis modulo p for every
sufficiently large prime p.