Square-free Lucas d-pseudoprimes and Carmichael-Lucas numbers

被引：0
|
作者：
Carlip, W. [1 ]
Somer, L.
机构：
[1] Franklin & Marshall Coll, Dept Math, Lancaster, PA 17604 USA
[2] Catholic Univ Amer, Dept Math, Washington, DC 20064 USA
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2007年 / 57卷 / 01期
关键词：
Lucas; Fibonacci; pseudoprime; Fermat;
D O I：
10.1007/s10587-007-0072-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let d be a fixed positive integer. A Lucas d-pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U(P, Q) such that the rank of N in U(P, Q) is exactly (N - epsilon(N))/d, where a is the signature of U(P, Q). We prove here that all but a finite number of Lucas d-pseudoprimes are square free. We also prove that all but a finite number of Lucas d-pseudoprimes are Carmichael-Lucas numbers.
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页码：447 / 463
页数：17
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