Preprint of "Only finitely many s-Cullen numbers are repunits for a fixed s≥2" on the math arXiv

A preprint of my paper with Michael Filaseta and Hester Graves, "Only finitely many s-Cullen numbers are repunits for a fixed s≥2" has appeared on the math arXiv. This is a sequel to an earlier paper with Hester, which proved that there were only finitely many solutions for all s, subject to the abc conjecture.

This proof is unconditional. I am now working on computations to extend 65536 to a much larger number -- it should be possible to get it into the millions.

"Proof of Two Conjectures of Andrica and Bagdasar" Appears in Integers

My paper, "Proof of Two Conjectures of Andrica and Bagdasar" has appeared in the journal Integers. It uses techniques from my earlier work to show that certain families of pseudoprimes are infinite. I hope that others find this technique useful.

Preprint of "Finding a Widely Digitally Delicate Prime" available on the math arXiv

In September, I posted a preprint of "Finding a Widely Digitally Delicate Prime" on the math arXiv. It may not end up published in this form, but because it described the only known example of such a prime, and how I found it, I wanted to have it documented.

"Ternary and Quaternary Curves of Small Fixed Genus and Gonality With Many Rational Points" Appears Online in Experimental Mathematics

 

My paper with Xander Faber, "Ternary and Quaternary Curves of Small Fixed Genus and Gonality With Many Rational Points," has appeared in Experimental Mathematics online. Based on my estimate of the journal's backlog, I expect print publication in 2023.

This is my tenth journal article published, although I may have to re-do the numbering in 2023.

"The abc Conjecture Implies That Only Finitely Many s-Cullen Numbers Are Repunits" Appears in the Journal of Integer Sequences

 

Catching up from earlier this year, my paper with Hester Graves, "The abc Conjecture Implies That Only Finitely Many s-Cullen Numbers Are Repunits" appeared in the Journal of Integer Sequences.

This is my ninth journal article published.

Preprint of "On Integers Whose Sum is the Reverse of their Product" available on the arXiv

 

The preprint of "On Integers Whose Sum is the Reverse of their Product", feat. Xander Faber is now available on the math arXiv.

Have you ever noticed that 9+9=18, while 9x9=81, which is 18 backwards? My co-author's kids did. The question of what other pairs of numbers a and b have a+b equal to axb backwards led us to write this paper. We give a technique for solving it in all bases. We have seen a list of these numbers in base 10 on the web, but we are aware of no other proof.

"A recent conjecture by Faber-Grantham"

What's even better than writing a paper? Having someone else write one answering a question you asked. In "Ternary and Quaternary Curves of Small Fixed Genus and Gonality with Many Rational Points," Xander Faber and I conjectured:

In a recent preprint, Floris Vermeulen proved this conjecture.