Catalan and Apéry numbers in residue classes

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Catalan and Apéry numbers in residue classes

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 seq...

متن کامل

Apéry Numbers and Central Trinomial Coefficients 3

Define the Apéry polynomial of degree n by A n (x) = n k=0 n k 2 n + k k 2. We determine p−1 k=0 (−1) k A k (1/4) and p−1 k=0 (−1) k A k (1/16) modulo a prime p > 3. Let b and c be integers and let the generalized trinomial coefficient T n (b, c) be the coefficient of x n in the expansion of (x 2 +bx+c) n. We establish the following new congruence p−1 k=0 T k (b, c) 2 (b 2 − 4c) k ≡ c(b 2 − 4c)...

متن کامل

Coincidences of Catalan and Q-catalan Numbers

Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday

متن کامل

Parametric Catalan Numbers and Catalan Triangles

Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schröder numbers and small Sch...

متن کامل

Paperfolding and Catalan numbers

1 : This paper reproves a few results concerning paperfolding sequences using properties of Catalan numbers modulo 2. The guiding principle can be described by: Paperfolding = Catalan modulo 2 + signs given by 2−automatic sequences.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series A

سال: 2006

ISSN: 0097-3165

DOI: 10.1016/j.jcta.2005.08.003