Cedar Crest College

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20182025

most citedMonogenic Quartic Polynomials and Their Galois Groups

6 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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math.NT2025

A further investigation on covering systems with odd moduli

Chris Bispels, Matthew Cohen, Joshua Harrington +4

Erdős first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific condition…

math.NT2024★ 6 cited

Monogenic Quartic Polynomials and Their Galois Groups

Joshua Harrington, Lenny Jones

A monic polynomial $f (x) \in Z [x]$ of degree $N$ is called monogenic if $f (x)$ is irreducible over $Q$ and ${1, θ, θ^{2}, \dots, θ^{N - 1}}$ is a basis for the ring…

math.NT2023

Arithmetic progressions of integers that are relatively prime to their digital sums

Ryan Blau, Joshua Harrington, Sarah Lohrey +2

For an integer $b \geq 2$ , we call a positive integer $b$ -anti-Niven if it is relatively prime to the sum of the digits in its base- $b$ representation. In this article, we investiga…

math.NT2023★ 2 cited

Every arithmetic progression contains infinitely many $b$ -Niven numbers

Joshua Harrington, Matthew Litman, Tony W. H. Wong

For an integer $b \geq 2$ , a positive integer is called a $b$ -Niven number if it is a multiple of the sum of the digits in its base- $b$ representation. In this article, we show that…

math.NT2021★ 1 cited

Covering systems with odd moduli

Joshua Harrington, Yewen Sun, Wing Hong Tony Wong

The concept of a covering system was first introduced by Erdős in 1950. Since their introduction, a lot of the research regarding covering systems has focused on the existence of c…

math.NT2021

Residue sums of Dickson polynomials over finite fields

Thomas Brazelton, Joshua Harrington, Matthew Litman +1

Given a polynomial with integral coefficients, one can inquire about the possible residues it can take in its image modulo a prime $p$ . The sum over the distinct residues can somet…

math.NT2020

On the properties of fibotomic polynomials

Cameron Byer, Tyler Dvorachek, Emily Eckard +3

Define the $n$ -th fibotomic polynomial to be the product of the monic irredicible factors of the $n$ -th Fibonacci polynomial which are not factors of any Fibonacci polynomial of sm…

math.NT2018★ 1 cited

An Investigation on Partitions with Equal Products

Byungchul Cha, Adam Claman, Joshua Harrington +6

An ordered triple $(s, p, n)$ is called admissible if there exist two different multisets $X = {x_{1}, x_{2}, \dots, x_{n}}$ and $Y = {y_{1}, y_{2}, \dots, y_{n}}$ such that $X$ and $Y$ share the sa…