Michael Filaseta

activity

20212023

collaborators

4 papers

math.NT2023

A generalization of a fourth irreducibility theorem of I. Schur

Martha Allen, Michael Filaseta

Let $u_{2 j}$ be the product of the odd positive integers $< 2 j$ . For $n$ an integer $\geq 1$ , define \[ f(x)=\sum_{j=0}^{n}a_j\frac{x^{2j}}{u_{2j+2}}, \] where the $a_{j}$ 's are arbit…

math.NT2023

Generalized Sierpiński Numbers

Michael Filaseta, Robert Groth, Thomas Luckner

A Sierpiński number is a positive odd integer $k$ such that $k \cdot 2^{n} + 1$ is composite for all positive integers $n$ . Fix an integer $A$ with $2 \leq A$ . We show that there exis…

math.NT2022

On the Factorization of lacunary polynomials

Michael Filaseta

This paper addresses the factorization of polynomials of the form $F (x) = f_{0} (x) + f_{1} (x) x^{n} + \dots + f_{r - 1} (x) x^{(r - 1) n} + f_{r} (x) x^{r n}$ where $r$ is a fixed positiv…

math.NT2021

Only finitely many $s$ -Cullen numbers are repunits for a fixed $s \geq 2$

Michael Filaseta, Jon Grantham, Hester Graves

We show that for any integer $s \geq 2$ , there are only finitely many $s$ -Cullen numbers that are repunits. More precisely, for fixed $s \geq 2$ , there are only finitely many intege…

A generalization of a fourth irreducibility theorem of I. Schur

Generalized Sierpiński Numbers

On the Factorization of lacunary polynomials

Only finitely many s-Cullen numbers are repunits for a fixed s≥2

Only finitely many $s$ -Cullen numbers are repunits for a fixed $s \geq 2$