On the prime density of Lucas sequences
Journal de Théorie des Nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 449-459.

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

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

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author = {Pieter Moree},
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},
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year = {1996},
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mrnumber = {1438482},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.181/}
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Pieter Moree. On the prime density of Lucas sequences. Journal de Théorie des Nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 449-459. doi : 10.5802/jtnb.181. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.181/

[1] C. Ballot, Density of prime divisors of linear recurrences, Mem. of the Amer. Math. Soc. 551, 1995. | MR: 1257079 | Zbl: 0827.11006

[2] F. Halter-Koch, Arithmetische Theorie der Normalkörper von 2-Potenzgrad mit Diedergruppe, J. Number Theory 3 (1971), 412-443. | MR: 285511 | Zbl: 0229.12006

[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: 205975 | Zbl: 0139.27501

[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: 789184 | Zbl: 0569.10003

[5] P. Moree, Counting divisors of Lucas numbers, MPI-preprint, no. 34, Bonn, 1996. | MR: 1663806

[6] R.W.K. Odoni, A conjecture of Krishnamurty on decimal periods and some allied problems, J. Number Theory 13 (1981), 303-319. | MR: 634201 | Zbl: 0471.10031

[7] P. Ribenboim, The book of prime number records, Springer-Verlag, Berlin etc., 1988. | MR: 931080 | Zbl: 0642.10001

[8] P. Ribenboim, Catalan's conjecture, Academic Press, Boston etc., 1994. | MR: 1259738 | Zbl: 0824.11010

[9] P. Stevenhagen, The number of real quadratic fields having units of negative norm, Experimental Mathematics 2 (1993), 121-136. | MR: 1259426 | Zbl: 0792.11041

[10] K. Wiertelak, On the density of some sets of primes. IV, Acta Arith. 43 (1984), 177-190. | MR: 736730 | Zbl: 0531.10049

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