J. Harrington

activity

20182026

most citedMonogenic Quartic Polynomials and Their Galois Groups

6 citations · 10 across the 12 of their papers we have counts for

collaborators

Showing 2026 · math.NTShow all

3 papers · 2 filters

math.NT2026

Generalized Wieferich primes and monogenic trinomials

Amy Falk, Joshua Harrington, Lenny Jones

Let $b \geq 2$ be an integer and let $p \geq 3$ be a prime. We say that $p$ is a {\em generalized Wieferich prime base $b$ }, or more succinctly, a {\em base- $b$ Wieferich prime,} if $b…

math.NT2026

Covering systems where the prime divisors of all moduli are only $2$ , $3$ , or $5$

Joshua Harrington, Jonah Klein, Joshua Lowrance +1

We try to find all quadruples of positive integers $(m, a, b, c)$ with $a \geq b \geq c$ such that there exists a distinct covering system with minimum modulus $m$ and least common mu…

math.NT2026

On the monogenicity and Galois groups of $x^{2 p} + a x^{p} + b^{p}$

Joshua Harrington, Lenny Jones

Let $f (x) = x^{2 p} + a x^{p} + b^{p}$ , where $p$ is a prime and $a, b \in Z$ with $ab \neq = 0$ . If $f (x)$ is irreducible over $Q$ , we say that $f (x)$ is monogenic if $\{1,θ,θ^2…

Generalized Wieferich primes and monogenic trinomials

Covering systems where the prime divisors of all moduli are only 2, 3, or 5

On the monogenicity and Galois groups of x2p+axp+bp

Covering systems where the prime divisors of all moduli are only $2$ , $3$ , or $5$

On the monogenicity and Galois groups of $x^{2 p} + a x^{p} + b^{p}$