Some Properties of Convolved k-Fibonacci Numbers

Convoluted convolved Fibonacci numbers

The convolved Fibonacci numbers F (r) j are defined by (1 − x − x2)−r =

Some Properties of Fibonacci Numbers

We formalized some basic properties of the Fibonacci numbers using definitions and lemmas from [7] and [23], e.g. Cassini’s and Catalan’s identities. We also showed the connections between Fibonacci numbers and Pythagorean triples as defined in [31]. The main result of this article is a proof of Carmichael’s Theorem on prime divisors of prime-generated Fibonacci numbers. According to it, if we ...

On the Properties of k-Fibonacci Numbers

Some Asymptotic Properties of Generalized Fibonacci Numbers

1. INTRODUCTION Horadam [1] has generalized two theorems of Subba Rao [3] which deal with some asymptotic p r o p e r t i e s of Fibonacci numbers. Horadam defined a sequence {w (n 2) where a , a are the roots of x 2-P 21 x + P 2 2 = 0. We shall let 06 """ LX r\ r\ UO r\-| • Horadam established two theorems for {w n }: I. The number of terms of {w n } not exceeding N is asymptotic to log(Nd/(P ...

On the properties of k-Fibonacci and k-Lucas numbers

In this paper, some properties of k−Fibonacci and k−Lucas numbers are derived and proved by using matrices S = k 2 1 2 k 2+4 2 k 2 and M = 