Lenny Jones

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20232026

most citedMonogenic Cyclic Quartic Trinomials

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math.NT2026

Generalized Wieferich primes and monogenic polynomials

Lenny Jones

Let $b, p \in Z$ with $b \geq 2$ and $p \geq 3$ a prime. If $b^{p - 1} \equiv 1 (mod p^{2})$ , then $p$ is called a {\em generalized Wieferich prime base $b$ }, or more succinctly,…

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

A Note on Abelian Monogenic Trinomials

Lenny Jones

An abelian monogenic polynomial $f (x) \in Z [x]$ is a monic polynomial of degree $N$ that is irreducible over $Q$ , such that the Galois group of $f (x)$ over ${\ma…

math.NT2026

Wieferich Primes and Monogenic Trinomials

Lenny Jones

A prime $p$ is called a Wieferich prime if $2^{p - 1} \equiv 1 (mod p^{2})$ . A monic polynomial $f (x) \in Z [x]$ of degree $N \geq 2$ is called monogenic if $f (x)$ is irreducible…

math.NT2026

Characterizing monogenic trinomials $x^{12} + a x^{6} + b$ according to their Galois groups

Lenny Jones

Let $f (x) = x^{12} + a x^{6} + b \in Z [x]$ , with $ab \neq = 0$ . We say that $f (x)$ is {\em monogenic} if $f (x)$ is irreducible over $Q$ and ${1, θ, θ^{2}, \dots, θ^{11}}$ is a…

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 polynomials

Generalized Wieferich primes and monogenic trinomials

A Note on Abelian Monogenic Trinomials

Wieferich Primes and Monogenic Trinomials

Characterizing monogenic trinomials x12+ax6+b according to their Galois groups

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

Characterizing monogenic trinomials $x^{12} + a x^{6} + b$ according to their Galois groups

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