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Catalan and Apéry numbers in residue classes
- Source :
-
Journal of Combinatorial Theory - Series A . Jul2006, Vol. 113 Issue 5, p851-865. 15p. - Publication Year :
- 2006
-
Abstract
- Abstract: 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 elements of each sequence already fall in all residue classes modulo every sufficiently large p, which improves the previously known result requiring 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. [Copyright &y& Elsevier]
- Subjects :
- *BINOMIAL coefficients
*BINOMIAL theorem
*MATHEMATICAL combinations
*POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 113
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 20980876
- Full Text :
- https://doi.org/10.1016/j.jcta.2005.08.003