On Some Special Property of The Farey Sequence

Authors

  • Ripan Saha Department of Mathematical Sciences, Raiganj University, University Road-733134, India

DOI:

https://doi.org/10.15415/mjis.2019.72016

Keywords:

Farey sequence, Palindrome, Euler’s Totient function

Abstract

In this paper, some special property of the Farey sequence is discussed. We prove in each term of the Farey sequence, the sum of elements in the denominator is two times of the sum of elements in the numerator. We also prove that the Farey sequence contains a palindrome structure.

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References

Ainsworth, J., Dawson, M., Pianta, J. and Warwick, J.(2012). “The farey sequence,” https://www.maths.ed.ac.uk/v1ranick/fareyproject.pdf.

Burton, D. M. (1980). Elementary Number Theory, Allyn and Bacon, Inc., pp.150.

Cobeli, C. and Zaharescu, A. (2003). “The Haros-Farey sequence at two hundred years,”Acta Univ. Apulensis Math. Inform, 5, 1–38.

Hatcher, A. Topology of numbers, Chapter 1, http://www.math.cornell.ed/hatcher .

Hardy, G. H. and Wright, E. M. (1979). An Introduction to the Theory of Numbers, The Clarendon Press, Oxford University Press, New York, Fifth edition.

Kanemitsu, S. and Yoshimoto, M. (1996). Farey series and the Riemann hypothesis, Acta Arith., 75. 4, 351–374.

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Published

2019-03-06

How to Cite

Ripan Saha. 2019. “On Some Special Property of The Farey Sequence”. Mathematical Journal of Interdisciplinary Sciences 7 (2):121-23. https://doi.org/10.15415/mjis.2019.72016.

Issue

Vol. 7 No. 2 (2019)

Section

Articles

License

 

Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.

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Creative Commons License Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in
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