Catalan and Apéry numbers in residue classes
نویسندگان
چکیده
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, for example, for Apéry numbers. We show that such sequences form a finite additive basis modulo p for every sufficiently large prime p.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 113 شماره
صفحات -
تاریخ انتشار 2006