Well, I'd say I didn't know you didn't know, only I have no idea who you are, so. :P
I mean to be clear the paper isn't 8 years old, just the theorems. Juan Arias de Reyna and I came up with two different proofs of Conjecture 8 and Conjecture 2 way back then, but, for various reasons, we didn't get it written up until now. If you're wondering which of the two proofs we used, though -- the answer is neither! We went with a third proof I only came up with a few months ago. Our older proofs were much worse. :P
Also, in writing this up, it became clear that although I'd written down the "off-by-one" theorem in my notes to Arias de Reyna, I'd never actually fully proven it; actually proving it involved a number of details I simply hadn't considered at the time.
no subject
Date: 2021-11-03 01:31 am (UTC)I mean to be clear the paper isn't 8 years old, just the theorems. Juan Arias de Reyna and I came up with two different proofs of Conjecture 8 and Conjecture 2 way back then, but, for various reasons, we didn't get it written up until now. If you're wondering which of the two proofs we used, though -- the answer is neither! We went with a third proof I only came up with a few months ago. Our older proofs were much worse. :P
Also, in writing this up, it became clear that although I'd written down the "off-by-one" theorem in my notes to Arias de Reyna, I'd never actually fully proven it; actually proving it involved a number of details I simply hadn't considered at the time.