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On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications

Author

Listed:
  • Monther Rashed Alfuraidan

    (Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Ibrahim Nabeel Joudah

    (Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

Abstract

In this work, we obtain a new formula for Fibonacci’s family m -step sequences. We use our formula to find the n th term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recurrence m -step relations with constant coefficients by using the last few terms of its corresponding Fibonacci’s family m -step sequence. As a computational number theory application, we develop a method to estimate the square roots.

Suggested Citation

  • Monther Rashed Alfuraidan & Ibrahim Nabeel Joudah, 2019. "On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications," Mathematics, MDPI, vol. 7(9), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:805-:d:262988
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