Original Research Article

Article volume = 2022 and issue = 1

Pages: 90–93

Article publication Date: November 21, 2022

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# Some Conjectures on Average of Fibonacci and Lucas Sequences

#### Daniel Yaqubi(a) and Amirali Fatehizadeh(b)

(a) Department of Computer Science, University of Torbat e Jam, Iran.

(b) Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran.

##### Abstract:

The arithmetic mean of the first n Fibonacci numbers is not an integer for all n. However, for some values of n we can observe that it is an integer. In this paper we consider the sequence of integers n for that the average of the first n Fibonacci numbers is an integer. We prove some interesting properties and present two related conjectures.

##### Keywords:

Fibonacci number, Lucas number, Pisano period, rank of appearance, restricted period.

##### References:

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##### Cite this article as:

- Daniel Yaqubi and Amirali Fatehizadeh, Some Conjectures on Average of Fibonacci and Lucas Sequences, Communications in Combinatorics, Cryptography & Computer Science, 2022(1), PP.90–93, 2022
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