Arithmetic properties of the sequence of derangements

被引：6

作者：

Miska, Piotr ^{[1
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Inst Math, Krakow, Poland

来源：

JOURNAL OF NUMBER THEORY | 2016年 / 163卷

关键词：

Derangement; Hensel's lemma; p-adic valuation; Periodicity; Prime number; FACTORIALS; SUMS;

D O I：

10.1016/j.jnt.2015.11.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The sequence of derangements is given by the formula D-0 = 1, D-n = nD(n-1) + (-1)(n) n > 0. It is a classical object appearing in combinatorics and number theory. In this paper we consider such arithmetic properties of the sequence of derangements as: periodicity modulo d, where d is an element of N+, p-adic valuations and prime divisors. Next, we use them to establish arithmetic properties of the sequences of even and odd derangements. (c) 2016 Elsevier Inc. All rights reserved.

引用

页码：114 / 145

页数：32

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