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

Title:

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

Creator:

Carlip, Walter and Somer, Lawrence

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:15ea6d1a-2e48-4fe6-a792-2d3c876c4a73
uuid:15ea6d1a-2e48-4fe6-a792-2d3c876c4a73

Subject:

Lucas, Fibonacci, pseudoprime, and Fermat

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $(N - \varepsilon (N))/d$, where $\varepsilon $ 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

447-463

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:1

Harvested from:

CDK

Metadata only:

false