后触点同余

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。

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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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