Prime divisors of Lucas sequences

Pieter Moree; Peter Stevenhagen

Acta Arithmetica (1997)

  • Volume: 82, Issue: 4, page 403-410
  • ISSN: 0065-1036

How to cite


Pieter Moree, and Peter Stevenhagen. "Prime divisors of Lucas sequences." Acta Arithmetica 82.4 (1997): 403-410. <>.

author = {Pieter Moree, Peter Stevenhagen},
journal = {Acta Arithmetica},
keywords = {Lucas sequence; Chebotarev density theorem; prime divisors; real quadratic field; fundamental unit},
language = {eng},
number = {4},
pages = {403-410},
title = {Prime divisors of Lucas sequences},
url = {},
volume = {82},
year = {1997},

AU - Pieter Moree
AU - Peter Stevenhagen
TI - Prime divisors of Lucas sequences
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 4
SP - 403
EP - 410
LA - eng
KW - Lucas sequence; Chebotarev density theorem; prime divisors; real quadratic field; fundamental unit
UR -
ER -


  1. [1] C. Ballot, Density of prime divisors of linear recurrences, Mem. Amer. Math. Soc. 551 (1995). 
  2. [2] H. Hasse, Über 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. Zbl0139.27501
  3. [3] 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. Zbl0569.10003
  4. [4] P. Moree, On the prime density of Lucas sequences, J. Théor. Nombres Bordeaux 8 (1996), 449-459. Zbl0873.11058
  5. [5] P. Ribenboim, The New Book of Prime Number Records, Springer, New York, 1995. Zbl0856.11001
  6. [6] P. Stevenhagen, Prime densities for second order torsion sequences, preprint. 

Citations in EuDML Documents

  1. Stefan Kühnlein, Some families of finite groups and their rings of invariants
  2. Christian Ballot, Counting monic irreducible polynomials P in 𝔽 q [ X ] for which order of X ( mod P ) is odd
  3. Christian Ballot, Strong arithmetic properties of the integral solutions of X³ + DY³ + D²Z³ - 3DXYZ = 1, where D = M³ ± 1, M ∈ ℤ*
  4. Pieter Moree, Peter Stevenhagen, Prime divisors of the Lagarias sequence
  5. Hans Roskam, Prime divisors of linear recurrences and Artin's primitive root conjecture for number fields

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