Let a and b be coprime positive integers. Then the number a+b divides the binomial coefficient ${a+b \choose a}$. I know how to prove this combinatorially - for example after choosing an ordered set of a+b elements, there is a free action of a cyclic group of order a+b on the set of a-element sub...
The Stone–Čech Compactification of $\mathbb{N}$ as a discrete space has been extensively studied and can be represented using ultrafilters.
Consider $X=(\mathbb{Z},\mathcal{T})$, where $\mathcal{T}$ is the Fürstenberg topology generated by arithmetic sequences. Equipped with this exotic topology...
Of course, since the question has been bumped, the tag now can (should) be removed.
The oldest version I see in the internet archive is from 2014 and it already contains the tag-removed tag.
I suppose it should be possible to download somehow older data dump and check there.
Ignoring the fact that I haven't done something like this yet - so I would have to learn how to work this data dump - I am not sure whether they are available also for MO.
I know that they are available on Internet Archive for Stack Exchange sites: stackoverflow.blog/2014/01/23/… I am not sure where MathOverflow content has been archived in this form (or some other form) before MO joined the SE network.
