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

Voir la notice de l'article

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 
@article{CMJ_2007_57_1_a33,
     author = {Carlip, W. and Somer, L.},
     title = {Square-free {Lucas} $d$-pseudoprimes and {Carmichael-Lucas} numbers},
     journal = {Czechoslovak Mathematical Journal},
     pages = {447--463},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309977},
     zbl = {1174.11016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a33/}
}
TY  - JOUR
AU  - Carlip, W.
AU  - Somer, L.
TI  - Square-free Lucas $d$-pseudoprimes and Carmichael-Lucas numbers
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 447
EP  - 463
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a33/
LA  - en
ID  - CMJ_2007_57_1_a33
ER  - 
%0 Journal Article
%A Carlip, W.
%A Somer, L.
%T Square-free Lucas $d$-pseudoprimes and Carmichael-Lucas numbers
%J Czechoslovak Mathematical Journal
%D 2007
%P 447-463
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a33/
%G en
%F CMJ_2007_57_1_a33
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/