On the prime density of Lucas sequences

Pieter Moree

Pieter Moree

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

Abstract (VO)
Résumé

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.

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.

MR Zbl

@article{JTNB_1996__8_2_449_0,
     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},
     volume = {8},
     number = {2},
     year = {1996},
     zbl = {0873.11058},
     mrnumber = {1438482},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_449_0/}
}

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

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