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
收藏
页码：114 / 145
页数：32
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