Friday, September 03, 2021

"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.

Monday, February 08, 2021

"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.