A note on the length of some finite continued fractions

Khalil Ayadi and Chiheb Ben Bechir
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 2, Pages 372–377
DOI: 10.7546/nntdm.2023.29.2.372-377
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Authors and affiliations

Khalil Ayadi
Sfax University, Higher Institute of Industrial Management of Sfax, Tunisia

Chiheb Ben Bechir
Sfax University, Faculty of Sciences, Lab AGTS, Tunisia

Abstract

In this paper, based on a 2008 result of Lasjaunias, we compute the lengths of simple continued fractions for some rational numbers whose numerators and denominators are explicitly given.

Keywords

  • Continued fraction
  • Rational numbers

2020 Mathematics Subject Classification

  • 11A55
  • 11D68

References

  1. Ayadi, K., Ben Bechir, C., & Elouaer, I. (2021). On some continued fractions and series. Studia Scientiarum Mathematicarum Hungarica, 58(2), 230–245.
  2. Ayadi, K., & Lasjaunias, A. (2016). On a quartic equation and two families of
    hyperquadratic continued fractions in power series fields. Moscow Journal of Combinatorics and Number Theory, 6, 14–37.
  3. Corvaja, P., & Zannier, U. (2005). On the length of the continued fraction for values of quotients of power sums. Journal de Théorie des Nombres de Bordeaux, 17, 737–748.
  4. Lasjaunias, A. (2008). Continued fractions for hyperquadratic power series over finite field. Finite Fields and Their Applications, 14, 329–350.
  5. Mendès France, M. (1971–1972). Quelques problèmes relatifs à la théorie des fractions continues limitées. Séminaire Delange-Pisot-Poitou. Théorie des nombres, 16(1), 1–6.
  6. Mendès France, M. (1973). Sur les fractions continues limitées. Acta Arithmetica, 14, 207–215.
  7. Shallit, J. (1979). Simple continued fractions for some irrational numbers. Journal of Number Theory, 11, 209–217.
  8. Tongron, Y., Kanasri, N. R., & Laohakosol, V. (2021). The depth of continued fraction expansion for some classes of rational functions. Asian-European Journal of Mathematics, 14(03), Article 2150033.
  9. van der Poorten, A. J., & Shallit, J. (1993). A specialised continued fraction. Canadian Journal of Mathematics, 5, 1067–1079.

Manuscript history

  • Received: 15 August 2022
  • Revised: 10 March 2023
  • Accepted: 18 May 2023
  • Online First: 18 May 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Ayadi, K., & Ben Bechir, C. (2023). A note on the length of some finite continued fractions. Notes on Number Theory and Discrete Mathematics, 29(2), 372-377, DOI: 10.7546/nntdm.2023.29.2.372-377.

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