A. Mbirika

activity

20092025

most citedLattice point visibility on generalized lines of sight

19 citations · 31 across the 14 of their papers we have counts for

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9 papers · 1 filter

math.NT2025

Weighted sums of Lucas numbers of the first and second kind

aBa Mbirika

In the \textit{Fibonacci Quarterly} in 1964, C.~R.~Wall gave the following weighted sum of generalized Fibonacci numbers: $\sum_{i = 1}^{n} i G_{i} = n G_{n + 2} - G_{n + 3} + G_{3}$ , where $\…

math.NT2024

Period patterns, entry points, and orders in the Lucas sequences: theory and applications

Morgan Fiebig, aBa Mbirika, Jürgen Spilker

The goal of this paper is twofold: (1) extend theory on certain statistics in the Fibonacci and Lucas sequences modulo $m$ to the Lucas sequences $U := \left(U_n(p,q)\right)_{n \ge…

math.NT2023

Pell and associated Pell braid sequences as GCDs of sums of $k$ consecutive Pell, balancing, and related numbers

aBa Mbirika, Janee Schrader, Jürgen Spilker

We consider the greatest common divisor (GCD) of all sums of $k$ consecutive terms of a sequence $(S_{n})_{n \geq 0}$ where the terms $S_{n}$ come from exactly one of following six well…

math.NT2022

GCD of sums of $k$ consecutive squares of generalized Fibonacci numbers

aBa Mbirika, Jürgen Spilker

In 2021, Guyer and Mbirika gave two equivalent formulas that computed the greatest common divisor (GCD) of all sums of $k$ consecutive terms in the generalized Fibonacci sequence $…

math.NT2021

Tantalizing properties of subsequences of the Fibonacci sequence modulo 10

Dan Guyer, aBa Mbirika, Miko Scott

The Fibonacci sequence modulo $m$ , which we denote $(F_{m, n})_{n = 0}^{\infty}$ where $F_{m, n}$ is the Fibonacci number $F_{n}$ modulo $m$ , has been a well…

math.NT2021★ 2 cited

GCD of sums of $k$ consecutive Fibonacci, Lucas, and generalized Fibonacci numbers

Dan Guyer, aBa Mbirika

We explore the sums of $k$ consecutive terms in the generalized Fibonacci sequence $(G_{n})_{n \geq 0}$ given by the recurrence $G_{n} = G_{n - 1} + G_{n - 2}$ for all $n \geq 2…

math.NT2019★ 1 cited

An Euler phi function for the Eisenstein integers and some applications

Emily Gullerud, Aba Mbirika

The Euler phi function on a given integer $n$ yields the number of positive integers less than $n$ that are relatively prime to $n$ . Equivalently, it gives the order of the group o…

math.NT2018★ 2 cited

New methods to find patches of invisible integer lattice points

Austin Goodrich, Aba Mbirika, Jasmine Nielsen

It is a surprising fact that the proportion of integer lattice points visible from the origin is exactly $\frac{6}{π ^{2}}$ , or approximately 60 percent. Hence, approximately 40 perce…

math.NT2017★ 19 cited

Lattice point visibility on generalized lines of sight

Edray Herber Goins, Pamela E. Harris, Bethany Kubik +1

For a fixed $b \in N = {1, 2, 3, \dots}$ we say that a point $(r, s)$ in the integer lattice $Z \times Z$ is $b$ -visible from the origin if it lies on the gra…