E. Goedhart

activity

20132026

most citedDiophantine approximation and the equation (a^2 c x^k - 1)(b^2 c y^k - 1) = (abc z^k - 1)^2

2 citations · 3 across the 10 of their papers we have counts for

collaborators

11 papers

math.NT2026

Atoms in the Semigroup of Non-Negative Integer Matrices

Lindsay Dever, Eva G. Goedhart, Gregory S. Heilbrunn +1

In the semigroup $M_{2} (N_{0})^{∙}$ , two-by-two matrices with non-negative integer entries and non-zero determinant, we study the factorization of matrices into atoms, or…

math.NT2024

A tree approach to the happy function

Eva G. Goedhart, Yusuf Gurtas, Pamela E. Harris

In this article, we present a method to construct $e$ -power $b$ -happy numbers of any height. Using this method, we construct a tree that encodes these happy numbers, their heights,…

math.NT2023

Replicable functions arising from code-lattice VOAs fixed by automorphisms

Lea Beneish, Jennifer Berg, Eva Goedhart +3

We ascertain properties of the algebraic structures in towers of codes, lattices, and vertex operator algebras (VOAs) by studying the associated subobjects fixed by lifts of code a…

math.NT2023

On a simple quartic family of Thue equations over imaginary quadratic number fields

Benjamin Earp-Lynch, Bernadette Faye, Eva G. Goedhart +2

Let $t$ be any imaginary quadratic integer with $∣ t ∣ \geq 100$ . We prove that the inequality \[ |F_t(X,Y)| = | X^4 - t X^3 Y - 6 X^2 Y^2 + t X Y^3 + Y^4 | \leq 1 \] has only trivial…

math.NT2022

On the Diophantine equations of the form $λ_{1} U_{n_{1}} + λ_{2} U_{n_{2}} + \dots + λ_{k} U_{n_{k}} = w p_{1}^{z_{1}} p_{2}^{z_{2}} \dots p_{s}^{z_{s}}$

Eva Goedhart, Brian Ha, Lily McBeath +1

In this paper, we consider the Diophantine equation $λ_{1} U_{n_{1}} + \dots + λ_{k} U_{n_{k}} = w p_{1}^{z_{1}} \dots p_{s}^{z_{s}},$ where ${U_{n}}_{n \geq 0}$ is a fixed non-degenerate linear recurrenc…

math.NT2022

Prime rational functions over a field

Eva Goedhart, Omar Kihel, Jesse Larone

The aim of this paper is to provide sufficient conditions for when a polynomial or rational function over a field K is prime using its order of vanishing at infinity and the result…

math.NT2021★ 1 cited

Solving Quadratic and Cubic Diophantine Equations using 2-adic Valuation Trees

Maila Brucal-Hallare, Eva G. Goedhart, Ryan Max Riley +2

For fixed integers $D \geq 0$ and $c \geq 3$ , we demonstrate how to use $2$ -adic valuation trees of sequences to analyze Diophantine equations of the form $x^{2} + D = 2^{c} y$ and $x^3+D=2…

math.NT2019

Sequences of consecutive factoradic happy numbers

Joshua Carlson, Eva G. Goedhart, Pamela E. Harris

Given a positive integer $n$ , the factorial base representation of $n$ is given by $n = \sum_{i = 1}^{k} a_{i} \cdot i!$ , where $a_{k} \neq = 0$ and $0 \leq a_{i} \leq i$ for all $1 \leq i \leq k$ . For…

math.NT2014★ 2 cited

Diophantine approximation and the equation (a^2 c x^k - 1)(b^2 c y^k - 1) = (abc z^k - 1)^2

E. G. Goedhart, H. G. Grundman

We prove that the Diophantine equation (a^2 c x^k - 1)(b^2 c y^k - 1) = (abc z^k - 1)^2 has no solutions in positive integers with x, y, z > 1, k \geq 7 and a^2x^k \neq b^2y^k.

math.NT2014

On the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5

Eva G. Goedhart, Helen G. Grundman

We prove that for each odd prime p, positive integer alpha, and non-negative integers beta and gamma, the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5 has…

math.NT2013

On the Diophantine equation N X^2 + 2^L 3^M = Y^N