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Computing Partial Information out of Intractable One — The First Digit of 2n at Base 3 as an Example

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2420))

Abstract

The problem of finding 2n when n is given is mathematically trivial, but computationally intractable. We show how to compute the most significant digit of the ternary representation of 2n in polynomial time.

Supported by the Academy of Finland under grant 44087.

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References

  1. A. Baker: Transcendental Number Theory. Cambridge University Press (1975).

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  2. A. Gelfond: Sur les approximations des nombres transcendants par des nombres algébriques. Dokl. Acad. Sci. URSS 2, 177–182, (in russian and french) (1935).

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  3. G. Rhin: Approximants de Padé et mesures effectives d’irrationalité. Séminaire de Théorie des Nombres, Paris 1985–86, 155–164, Progr. Math., 71, Birkhäuser Boston, Boston, MA (1987).

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© 2002 Springer-Verlag Berlin Heidelberg

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Hirvensalo, M., Karhumäki, J. (2002). Computing Partial Information out of Intractable One — The First Digit of 2n at Base 3 as an Example. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_26

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  • DOI: https://doi.org/10.1007/3-540-45687-2_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44040-6

  • Online ISBN: 978-3-540-45687-2

  • eBook Packages: Springer Book Archive

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