1. Square-free Lucas $d$-pseudoprimes and Carmichael-Lucas numbers
- Creator:
- Carlip, Walter and Somer, Lawrence
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Lucas, Fibonacci, pseudoprime, and Fermat
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public