On a new formula for Fibonacci's family m-step numbers and some applications

Monther Rashed Alfuraidan; Ibrahim Nabeel Joudah

doi:10.3390/math7090805

On a new formula for Fibonacci's family m-step numbers and some applications

Monther Rashed Alfuraidan^*, Ibrahim Nabeel Joudah

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this work, we obtain a new formula for Fibonacci's family m-step sequences. We use our formula to find the nth 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.

Original language	English
Article number	805
Journal	Mathematics
Volume	7
Issue number	9
DOIs	https://doi.org/10.3390/math7090805
State	Published - 1 Sep 2019

Bibliographical note

Publisher Copyright:
© 2019 by the authors.

Keywords

Fibonacci's m-step numbers
Linear homogeneous recurrence relations
Time complexity

ASJC Scopus subject areas

General Mathematics

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10.3390/math7090805

Cite this

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abstract = "In this work, we obtain a new formula for Fibonacci's family m-step sequences. We use our formula to find the nth 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.",

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KW - Linear homogeneous recurrence relations

KW - Time complexity

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On a new formula for Fibonacci's family m-step numbers and some applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this