Archiv der Mathematik

, Volume 62, Issue 4, pp 300–305

Irrationality results for reciprocal sums of certain Lucas numbers

  • Paul -Georg Becker
  • Thomas Töpfer


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. André-Jeannin, A note on the irrationality of certain Lucas infinite series. Fibonacci Quart.29, 132–136 (1991).Google Scholar
  2. [2]
    C. Badea, The irrationality of certain infinite series. Glasgow Math. J.29, 221–228 (1987).Google Scholar
  3. [3]
    P.-G.Becker and T.Töpfer, Transcendency results for sums of reciprocals of linear recurrences. To appear in Math. Nachr.Google Scholar
  4. [4]
    P. Bundschuh undA. Pethö, Zur Transzendenz gewisser Reihen. Monatsh. Math.104, 199–223 (1987).Google Scholar
  5. [5]
    P.Bundschuh and K.Väänänen, Arithmetical investigations of a certain infinite product. To appear in Compositio Math.Google Scholar
  6. [6]
    P.Erdös and R. L.Graham, Old and new problems and results in combinatorial number theory. Genève 1980.Google Scholar
  7. [7]
    I. J. Good, A reciprocal series of Fibonacci numbers. Fibonacci Quart.12, 346 (1974).Google Scholar
  8. [8]
    V. E. Hoggatt Jr. andM. Bicknell, A reciprocal series of Fibonacci numbers with subscripts 2n k. Fibonacci Quart.14, 453–455 (1976).Google Scholar
  9. [9]
    K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen. Math. Ann.101, 342–366 (1929).Google Scholar
  10. [10]
    M. Mignotte, An application of W. Schmidt's theorem. Transcendental numbers and golden number. Fibonacci Quart.15, 15–16 (1977).Google Scholar
  11. [11]
    T. N. Shorey andC. L. Stewart, On the diophantine equationax 2t+bx t y+cy 2=d and pure powers in recurrence sequences. Math. Scand.52, 24–36 (1983).Google Scholar
  12. [12]
    T. N.Shorey and R.Tijdeman, Exponential diophantine equations. Cambridge 1986.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Paul -Georg Becker
    • 1
  • Thomas Töpfer
    • 1
  1. 1.Mathematisches Institut der Universität KölnKöln

Personalised recommendations