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Irrationality results for reciprocal sums of certain Lucas numbers

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References

  1. R. André-Jeannin, A note on the irrationality of certain Lucas infinite series. Fibonacci Quart.29, 132–136 (1991).

    Google Scholar 

  2. C. Badea, The irrationality of certain infinite series. Glasgow Math. J.29, 221–228 (1987).

    Google Scholar 

  3. P.-G.Becker and T.Töpfer, Transcendency results for sums of reciprocals of linear recurrences. To appear in Math. Nachr.

  4. P. Bundschuh undA. Pethö, Zur Transzendenz gewisser Reihen. Monatsh. Math.104, 199–223 (1987).

    Google Scholar 

  5. P.Bundschuh and K.Väänänen, Arithmetical investigations of a certain infinite product. To appear in Compositio Math.

  6. P.Erdös and R. L.Graham, Old and new problems and results in combinatorial number theory. Genève 1980.

  7. I. J. Good, A reciprocal series of Fibonacci numbers. Fibonacci Quart.12, 346 (1974).

    Google Scholar 

  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. K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen. Math. Ann.101, 342–366 (1929).

    Google Scholar 

  10. M. Mignotte, An application of W. Schmidt's theorem. Transcendental numbers and golden number. Fibonacci Quart.15, 15–16 (1977).

    Google Scholar 

  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. T. N.Shorey and R.Tijdeman, Exponential diophantine equations. Cambridge 1986.

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Author notes

  1. Paul -Georg Becker & Thomas Töpfer

    Present address: Mathematisches Institut der Universität Köln, Weyertal 86-90, D-50931, Köln

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    1. Paul -Georg Becker
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    2. Thomas Töpfer
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    Supported by a Habilitation Fellowship of the Deutsche Forschungsgemeinschaft.

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    Becker, P.G., Töpfer, T. Irrationality results for reciprocal sums of certain Lucas numbers. Arch. Math 62, 300–305 (1994). https://doi.org/10.1007/BF01201780

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