There's an update from Tao after emailing Tenenbaum (the paper author) about this:
> He speculated that "the formulation [of the problem] has been altered in some way"....
[snip]
> More broadly, I think what has happened is that Rogers' nice result (which, incidentally, can also be proven using the method of compressions) simply has not had the dissemination it deserves. (I for one was unaware of it until KoishiChan unearthed it.) The result appears only in the Halberstam-Roth book, without any separate published reference, and is only cited a handful of times in the literature. (Amusingly, the main purpose of Rogers' theorem in that book is to simplify the proof of another theorem of Erdos.) Filaseta, Ford, Konyagin, Pomerance, and Yu - all highly regarded experts in the field - were unaware of this result when writing their celebrated 2007 solution to #2, and only included a mention of Rogers' theorem after being alerted to it by Tenenbaum. So it is perhaps not inconceivable that even Erdos did not recall Rogers' theorem when preparing his long paper of open questions with Graham in 1980.
(emphasis mine)
I think the value of LLM guided literature searches is pretty clear!
This whole thread is pretty funny. Either it can demo some pretty clever, but still limited, features resulting in math skills OR it's literally the best search engine ever invented. My guess is the former, it's pretty whatever at web search and I'd expect to see something similar to the easily retrievable, more visible proof method from Rogers' (as opposed to some alleged proof hidden in some dataset).
Your point seemed to be, if Tao et al. haven't heard of it then it must not exist. The now known literature proof contradicts that claim.
There's an update from Tao after emailing Tenenbaum (the paper author) about this:
> He speculated that "the formulation [of the problem] has been altered in some way"....
[snip]
> More broadly, I think what has happened is that Rogers' nice result (which, incidentally, can also be proven using the method of compressions) simply has not had the dissemination it deserves. (I for one was unaware of it until KoishiChan unearthed it.) The result appears only in the Halberstam-Roth book, without any separate published reference, and is only cited a handful of times in the literature. (Amusingly, the main purpose of Rogers' theorem in that book is to simplify the proof of another theorem of Erdos.) Filaseta, Ford, Konyagin, Pomerance, and Yu - all highly regarded experts in the field - were unaware of this result when writing their celebrated 2007 solution to #2, and only included a mention of Rogers' theorem after being alerted to it by Tenenbaum. So it is perhaps not inconceivable that even Erdos did not recall Rogers' theorem when preparing his long paper of open questions with Graham in 1980.
(emphasis mine)
I think the value of LLM guided literature searches is pretty clear!
This whole thread is pretty funny. Either it can demo some pretty clever, but still limited, features resulting in math skills OR it's literally the best search engine ever invented. My guess is the former, it's pretty whatever at web search and I'd expect to see something similar to the easily retrievable, more visible proof method from Rogers' (as opposed to some alleged proof hidden in some dataset).