The Multiplication Operation of Two Continued Fractions with Positive Non Integer Numerators

Abstract

This paper is a sequel to our previous work in which we found a elementary arithmetic operators of simple continued fractions. We consider the continued fractions (C.F.). We found the multiplication operation of two continued fractions with positive non integer numerators. We apply our finding to many examples of continued fractions.

Country : Libya

1 Fatima F. Abdullah2 Souad I. Mugassabi

  1. University of Benghazi, Benghazi, Libya
  2. University of Benghazi, Benghazi, Libya

IRJIET, Volume 4, Issue 7, July 2020 pp. 14-19

doi.org/10.47001/IRJIET/2020.407003

References

  1. Alan Baker (1986). "A concise introduction to theory of numbers". Cambridge University press.
  2. Burton, D. M. (2006). "Elementary number theory". Tata McGraw-Hill Education.
  3. Greene, J., & Schmieg, J. (2017). "Continued Fractions with Non-Integer Numerators". J. Integer Seq., 20(1), 17-1.
  4. Hardy, G. H., Wright, E. M., Heath-Brown, R., Silverman, J., & Wiles, A. (2008). "An Introductionto the Theory of Numbers". Oxford University Press.
  5. LeVeque, W. J. (2014). "Fundamentals of Number Theory". Courier Corporation.
  6. Mugassabi S. and Amsheri S. (2020) . ''The Multiplication and Division of Simple Continued Fractions''. IJISM International Journal of Innovation in Science and Mathematics 8 (3): (2020) 2347–9051.
  7. Mugassabi, Souad I., and A. S. Elmabrok. (2019). "The Power of Simple Continued Fractions." EPH-International Journal of Applied Science (ISSN: 2208-2182) 1.1: 824-833.
  8. Mugassabi S. and Mistiri F. (2015). ''The Elementary Arithmetic Operators of Continued Fractions''. Am-Euras. J. Sci.Res.,10 (5): 251 - 263.
  9. C.D. Olds. (1963). ''Continued Fractions''. 5th Edition, New York: Random House, Inc.