So, a while ago I wrote here about the following open problem: Is there a finite coloring of the positive integers such that, for each (n,m)≠(2,2), n+m always gets a different color from nm? (With the expected answer being no.) In particular I wrote about a weaker variant suggested by ![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
joshuazelinsky; if one defines a greedy coloring obeying this latter constraint, can we at least show that this uses infinitely many colors? (Later I copied this entry to my website.)
Anyway, Josh informs me that the original problem is now solved! The paper is here.
I was going to take down the page on my website, but Josh said leave it up because it's not like everything has been resolved about his modified problem. In particular, it's still not clear what the growth rate of the function g is, nor if the interleaving pattern I observed holds up.
Anyway yay that's resolved!
And should hopefully have time to write about Mystery Hunt soon...
joshuazelinsky; if one defines a greedy coloring obeying this latter constraint, can we at least show that this uses infinitely many colors? (Later I copied this entry to my website.)Anyway, Josh informs me that the original problem is now solved! The paper is here.
I was going to take down the page on my website, but Josh said leave it up because it's not like everything has been resolved about his modified problem. In particular, it's still not clear what the growth rate of the function g is, nor if the interleaving pattern I observed holds up.
Anyway yay that's resolved!
And should hopefully have time to write about Mystery Hunt soon...
