Pacific Journal of Mathematics

The set of primes dividing the Lucas numbers has density $2/3$.

J. C. Lagarias

Article information

Source
Pacific J. Math., Volume 118, Number 2 (1985), 449-461.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102706452

Mathematical Reviews number (MathSciNet)
MR789184

Zentralblatt MATH identifier
0569.10003

Subjects
Primary: 11B05: Density, gaps, topology
Secondary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations

Citation

Lagarias, J. C. The set of primes dividing the Lucas numbers has density $2/3$. Pacific J. Math. 118 (1985), no. 2, 449--461. https://projecteuclid.org/euclid.pjm/1102706452


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References

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  • [2] B. J. Birch, Cyclotomic Fields and Kummer Extensions, in: Algebraic Number Fields (J. W. S. Cassels and A. Frohlich, Eds.), Academic Press, London 1967, 85-93.
  • [3] H. H. Hasse, fber die Dichte der Primzahlen p, fur die eine vorgegebeneganzrationale Zahl a 0 von gerader bzw. ungerader Ordung mod p ist., Math. Annalen, 168 (1966), 19-23.
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  • [5] J. C. Lagarias, Sets of primes determined by systems of polynomial congruences, Illinois J. Math, 27 (1983), 224-235.
  • [6] S. Lang, Algebraic Number Theory, Addison-Wesley Publ. Co, New York 1970.
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  • [11] R. W. K. Odoni, A conjecture of Krishnamurthy on decimal periods and some allied problems, J. Number Theory, 13 (1981), 303-319.
  • [12] W. Sierpinski, Sur une decomposition des numbers premiers en deux classes, Collect. Math, 10 (1958), 81-83. (Also: Problem 29, Elem. d. Math, 14 (1959), 60.)
  • [13] P. J. Stephens, Prime divisors of second order linear recurrences /., J. Number Theory 8 (1976), 313-332.
  • [14] P. J. Stephens, Prime divisors of second order linear recurrences II, J. Number Theory, 8 (1976), 333-345.
  • [15] M. Ward, Prime divisors of second order recurring sequences, Duke Math. J, 21 (1954), 178-188.
  • [16] M. Ward, The prime divisors of Fibonacci numbers, Pacific J. Math, 11 (1961), 379-386.

See also

  • Errata : J. C. Lagarias. Errata to: ``The set of primes dividing the Lucas numbers has density $2/3$''. Pacific Journal of Mathematics volume 162, issue 2, (1994), pp. 393-396.