Congruences for Bernoulli, Euler, and Stirling Numbers
نویسندگان
چکیده
منابع مشابه
Congruences for Bernoulli , Euler , and Stirling Numbers Paul
The values at x=0 are called Bernoulli and Euler numbers of order w; when w=1, the polynomials or numbers are called ordinary. When x=0 or w=1, we often suppress that part of the notation; e.g., B (w) n denotes B n (0), En(x) denotes E (1) n (x), and Bn denotes B (1) n (0). These numbers have been extensively studied and many congruences for them are known. Among the most important results are ...
متن کاملCongruences involving Bernoulli and Euler numbers
Let [x] be the integral part of x. Let p > 5 be a prime. In the paper we mainly determine P[p/4] x=1 1 xk (mod p2), p−1 [p/4] (mod p3), Pp−1 k=1 2 k (mod p3) and Pp−1 k=1 2 k2 (mod p2) in terms of Euler and Bernoulli numbers. For example, we have
متن کاملCongruences on Stirling Numbers and Eulerian Numbers
In this paper, we establish some Fleck-Weisman type congruences for the Stirling numbers and the Eulerian numbers.
متن کاملCongruences concerning Bernoulli numbers and Bernoulli polynomials
Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (modp), where p is an odd prime, x is a p-integral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=x ) (modp ); ∑(p−1)=2 x=1 (1=x ) (modp ); (p − 1)! (modp ) and Ar(m;p) (modp), where k ∈ {1; 2; : : : ; p− 1} and Ar(m;p) i...
متن کاملArith . COMBINATORIAL CONGRUENCES AND STIRLING NUMBERS
In this paper we obtain some sophisticated combinatorial con-gruences involving binomial coefficients and confirm two conjectures of the author and Davis. They are closely related to our investigation of the pe-riodicity of the sequence P l j=0ì j ´ S(j, m)a l−j (l = m, m + 1,. . .) modulo a prime p, where a and m > 0 are integers, and those S(j, m) are Stirling numbers of the second kind. We a...
متن کاملذخیره 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 Number Theory
سال: 1999
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2401