On Fibonacci Numbers and its Applications
Veena Narayanan1, R Venkat Ramanan2, R Srikanth3, L Likitha4

1R Venkat Ramanan, School of Mechanical Engineering, SASTRA Deemed University, Thanjavur, India.
2L Likhitha, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur, India.
3Veena Narayanan, Department of Mathematics, SASTRA Deemed University, Thanjavur, India.
4R Srikanth, Tata Realty-SASTRA Srinivasa Ramanujan Research chair professor for Number Theory, SASTRA Deemed University, Thanjavur, India. 

Manuscript received on September 16, 2019. | Revised Manuscript received on 24 September, 2019. | Manuscript published on October 10, 2019. | PP: 453-455 | Volume-8 Issue-12, October 2019. | Retrieval Number: L33371081219/2019©BEIESP| DOI: 10.35940/ijitee.L3337.1081219
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: In this article, we explore the representation of the product of k consecutive Fibonacci numbers as the sum of kth power of Fibonacci numbers. We also present a formula for finding the coefficients of the Fibonacci numbers appearing in this representation. Finally, we extend the idea to the case of generalized Fibonacci sequence and also, we produce another formula for finding the coefficients of Fibonacci numbers appearing in the representation of three consecutive Fibonacci numbers as a particular case. Also, we point out some amazing applications of Fibonacci numbers.
Keywords: Fibonacci Sequence, Generalized Fibonacci Sequence, Golden ratio, Linear Combination of Numbers.
Scope of the Article: Standards for IoT Applications