Geodesic
Square-free Lucas $d$-pseudoprimes and Carmichael-Lucas numbers
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 447-463 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 11A51, 11B37, 11B39
Keywords: Lucas; Fibonacci; pseudoprime; Fermat 
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Carlip, W.; Somer, L. Square-free Lucas $d$-pseudoprimes and Carmichael-Lucas numbers. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 447-463. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a33/

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