Square-free Lucas d-pseudoprimes and Carmichael-Lucas numbers |
| |
| Authors: | W. Carlip L. Somer |
| |
| Affiliation: | (1) Department of Mathematics, Franklin & Marshall College, Lancaster, Pennsylvania 17604, USA;(2) Department of Mathematics, Catholic University of America, Washington, D. C. 20064, USA |
| |
| Abstract: | 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 − ε(N))/d, where ε 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. |
| |
| Keywords: | Lucas Fibonacci pseudoprime Fermat |
| 本文献已被 SpringerLink 等数据库收录！ |
|
