Some results on infinite power towers

Mladen Vassilev-Missana
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 16, 2010, Number 3, Pages 18—24
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Authors and affiliations

Mladen Vassilev-Missana
5, V. Hugo Str., Sofia-1124, Bulgaria

Abstract

In the paper the infinite power towers which are generated by an algebraic numbers belonging to the closed interval 1,e^{\frac{1}{e}} are investigated and an answer is given to the question when they are transcendental or rational numbers. Also a necessary condition for an infinite power tower to be an irrational algebraic number is proposed.

Keywords

  • Infinite power tower
  • Algebraic number
  • Transcendental number

References

  1. Baker, A. Transcendental Number Theory. London, Cambridge University Press, 1990.
  2. Vassilev-Missana, M. A short remark on transcendental numbers. Notes on Number Theory and Discrete Mathematics, Vol. 14, No. 4, 2008, 1-3.
  3. Shkliarski D., N. Chentzov, I. Yaglom. The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics, New York, Dover Publications, 1993.

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Cite this paper

APA

Vassilev-Missana, M. (2010). Some results on infinite power towers. Notes on Number Theory and Discrete Mathematics, 16(3), 18-24.

Chicago

Vassilev-Missana, Mladen. “Some Results on Infinite Power Towers.” Notes on Number Theory and Discrete Mathematics 16, no. 3 (2010): 18-24.

MLA

Vassilev-Missana, Mladen. “Some Results on Infinite Power Towers.” Notes on Number Theory and Discrete Mathematics 16.3 (2010): 18-24. Print.

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