后触点同余

IF 0.4 4区数学 Q4 MATHEMATICS

Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2021-10-12 DOI:10.36045/j.bbms.210412a

G. Serafin

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引用次数: 0

摘要

著名的Touchard同余说明Bn+p≡Bn+ Bn+1模p，其中p是素数，Bn表示贝尔数。本文研究了Bn - p的可整除性质及其在p的高次幂和r-贝尔数中的推广。特别地，我们证明了所考虑的问题与Sun-Zagier同余的密切关系，并通过推导r-Bell与差数之间的新关系进一步改进了这一关系。最后，我们得到了关于贝尔数模p周期的一些结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Backward Touchard congruence

The celebrated Touchard congruence states that Bn+p ≡ Bn + Bn+1 modulo p, where p is a prime number and Bn denotes the Bell number. In this paper we study divisibility properties of Bn−p and their generalizations involving higher powers of p as well as the r-Bell numbers. In particular, we show a closely relation of the considered problem to the Sun-Zagier congruence, which is additionally improved by deriving a new relation between r-Bell and derangement numbers. Finally, we conclude some results on the period of the Bell numbers modulo p.

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来源期刊

Bulletin of the Belgian Mathematical Society-Simon Stevin 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.