Infinitude of k-Lehmer numbers which are not Carmichael

被引：1

作者：

McNew, Nathan ^{[1
]}

Wright, Thomas ^{[2
]}

机构：

[1] Towson Univ, Dept Math, 7800 York Rd, Towson, MD 21252 USA

[2] Wofford Coll, Dept Math, 429 N Church St, Spartanburg, SC 29302 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2016年 / 12卷 / 07期

关键词：

Lehmer numbers; Carmichael numbers; Euler totient function; primes in tuples;

D O I：

10.1142/S1793042116501153

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that there are infinitely many n's for which rad(phi(n))vertical bar n -1 but n is not a Carmichael number. Additionally, we prove that for any k >= 3, there exist infinitely many n's such that phi(n)vertical bar(n-1)(k) but phi(n) inverted iota (n-1)(k-1). The constructions that we consider here are generalizations of Carmichael and Lehmer numbers, respectively, that were first formulated by Grau and Oller-Marcen.

引用

页码：1863 / 1869

页数：7

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