Fibonacci numbers - Open Access .click

The American Mathematical Monthly, 2016
AbstractThere have been many articles in the MONTHLY on quotient sets over the years. We take a first step here into the p-adic setting, which we hope will spur further research.
Stephan Ramon Garcia, Florian Luca
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Factorization of Fibonacci Numbers

The Fibonacci Quarterly, 1970
The Fibonacci numbers \(F_n\) may be defined by \(F_0 = 0\), \(F_1= 1\), \(F_{n+1}=F_n +F_{n-1}\) for \(n \geq 1\). If \(F_z\) \(z>0\), is the smallest Fibonacci number divisible by the prime \(p\), then \(z =a(p)\) is defined as the entry point (or rank) of \(p\); moreover \(p\) divides \(F_n\) if and only if \(n\) is divisible by \(z(p)\).
Daykin, D. E., Dresel, L. A. G.
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On the Fibonacci k-numbers

Chaos, Solitons & Fractals, 2007
Q1
Falcón, Sergio, Plaza, Ángel
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Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers

Mathematica Slovaca
AbstractLet (Fn)n≥0and (Ln)n≥0be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations ofaandb, we mean the both concatenationsabandbatogether, whereaandbare any two nonnegative integers.
Altassan, Alaa, ALAN, Murat
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mathematics
recurrence relations
generating function

11b37
fibonacci sequence
fibonacci number

generating functions
11b39
generalized fibonacci numbers