University of Wisconsin–Eau Claire

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19962024

most citedModules for Experiments in Stellar Astrophysics (MESA): Time-Dependent Convection, Energy Conservation, Automatic Differentiation, and Infrastructure

599 citations

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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.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.NT2018★ 1 cited

Generating Bézout trees for Pythagorean pairs

Emily Gullerud, James S. Walker

Relatively prime pairs of integers can be represented as nodes in three way branching trees. We construct trees of Bézout coefficients which correspond to the relatively prime pair…

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…