TY - JOUR
T1 - Catalan and Apéry numbers in residue classes
AU - Garaev, Moubariz Z.
AU - Luca, Florian
AU - Shparlinski, Igor E.
PY - 2006/7
Y1 - 2006/7
N2 - 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 p13 / 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 pO ( p ) elements. We also study, using a different technique, similar questions for sequences satisfying polynomial recurrence relations like the Apéry numbers. We show that such sequences form a finite additive basis modulo p for every sufficiently large prime p.
AB - 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 p13 / 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 pO ( p ) elements. We also study, using a different technique, similar questions for sequences satisfying polynomial recurrence relations like the Apéry numbers. We show that such sequences form a finite additive basis modulo p for every sufficiently large prime p.
UR - http://www.scopus.com/inward/record.url?scp=33646778853&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2005.08.003
DO - 10.1016/j.jcta.2005.08.003
M3 - Article
AN - SCOPUS:33646778853
VL - 113
SP - 851
EP - 865
JO - Journal of Combinatorial Theory: Series A
JF - Journal of Combinatorial Theory: Series A
SN - 1096-0899
IS - 5
ER -