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

Monther Rashed Alfuraidan and Ibrahim Nabeel Joudah
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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

Mathematics, 2019, vol. 7, issue 9, 1-9

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.

Keywords: Fibonacci’s m -step numbers; time complexity; linear homogeneous recurrence relations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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