On the prime density of Lucas sequences

Moree, Pieter

Moree, Pieter

Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 449-459.

Résumé
Abstract

On donne la densité des nombres premiers qui divisent au moins un terme de la suite de Lucas ${\{L_{n} (P)\}}_{n = 0}^{\infty}$ , définie par $L_{0} (P) = 2, L_{1} (P) = P$ et $L_{n} (P) = P L_{n - 1} (P) + L_{n - 2} (P)$ pour $n \geq 2$ , avec $P$ entier arbitraire.

The density of primes dividing at least one term of the Lucas sequence ${\{L_{n} (P)\}}_{n = 0}^{\infty}$ , defined by $L_{0} (P) = 2, L_{1} (P) = P$ and $L_{n} (P) = P L_{n - 1} (P) + L_{n - 2} (P)$ for $n \geq 2$ , with $P$ an arbitrary integer, is determined.

MR Zbl | 1 citation dans Numdam

@article{JTNB_1996__8_2_449_0,
     author = {Moree, Pieter},
     title = {On the prime density of {Lucas} sequences},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {449--459},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     year = {1996},
     mrnumber = {1438482},
     zbl = {0873.11058},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1996__8_2_449_0/}
}

TY  - JOUR
AU  - Moree, Pieter
TI  - On the prime density of Lucas sequences
JO  - Journal de théorie des nombres de Bordeaux
PY  - 1996
SP  - 449
EP  - 459
VL  - 8
IS  - 2
PB  - Université Bordeaux I
UR  - http://www.numdam.org/item/JTNB_1996__8_2_449_0/
LA  - en
ID  - JTNB_1996__8_2_449_0
ER  -

%0 Journal Article
%A Moree, Pieter
%T On the prime density of Lucas sequences
%J Journal de théorie des nombres de Bordeaux
%D 1996
%P 449-459
%V 8
%N 2
%I Université Bordeaux I
%U http://www.numdam.org/item/JTNB_1996__8_2_449_0/
%G en
%F JTNB_1996__8_2_449_0

Moree, Pieter. On the prime density of Lucas sequences. Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 449-459. http://www.numdam.org/item/JTNB_1996__8_2_449_0/

Bibliographie
Cité par

[1] C. Ballot, Density of prime divisors of linear recurrences, Mem. of the Amer. Math. Soc. 551, 1995. | MR | Zbl

[2] F. Halter-Koch, Arithmetische Theorie der Normalkörper von 2-Potenzgrad mit Diedergruppe, J. Number Theory 3 (1971), 412-443. | MR | Zbl

[3] H. Hasse, Uber die Dichte der Primzahlen p, für die eine vorgegebene ganzrationale Zahl a ≠ 0 von gerader bzw., ungerader Ordnung mod. p ist, Math. Ann. 166 (1966), 19-23. | MR | Zbl

[4] J.C. Lagarias, The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math. 118 (1985), 449-461 (Errata, Pacific J. Math. 162 (1994), 393-397). | MR | Zbl

[5] P. Moree, Counting divisors of Lucas numbers, MPI-preprint, no. 34, Bonn, 1996. | MR

[6] R.W.K. Odoni, A conjecture of Krishnamurty on decimal periods and some allied problems, J. Number Theory 13 (1981), 303-319. | MR | Zbl

[7] P. Ribenboim, The book of prime number records, Springer-Verlag, Berlin etc., 1988. | MR | Zbl

[8] P. Ribenboim, Catalan's conjecture, Academic Press, Boston etc., 1994. | MR | Zbl

[9] P. Stevenhagen, The number of real quadratic fields having units of negative norm, Experimental Mathematics 2 (1993), 121-136. | MR | Zbl

[10] K. Wiertelak, On the density of some sets of primes. IV, Acta Arith. 43 (1984), 177-190. | MR | Zbl