Which journals publish 1-page papers Having read a thread on a similar question on expository papers I'm reminded of reason #99 to drop my math PhD thingy, late c20th: I just couldn't blow up this paper to 4 pages. (OK, one half-page calculation was left to the expert reader (and other experts could guess), but...)
 A: Proceedings of the AMS likes short papers. Looking at their most recent table of contents, I see between 4-13, with the median probably around 9. I think they would be open to a 1 page paper.
A: A lower bound on paper length would make little sense - if something can be proved very quickly, but the proof is novel and the result is interesting enough to justify the publishing process, then so much the better.  (With very important results, sometimes you'll even see papers in well-regarded journals entitled 'A Short Proof of (already known result)', because short, clear proofs are valuable even when other proofs are known.)  One note of caution though: if you are a 'hobby mathematician' as you say in your profile, and you have an unusual writing style, you may have to work extra hard to overcome the referee's scepticism.  This is a reason to write more detail rather than less, especially in the initial submission.  You can always trim it down later if that's what the journal wants.
A: I just stumbled across a very recent example (2017) at the Archiv der Mathematik which I felt compelled to add to this list.
A: There are plenty of examples listed here.
A: Generally, journals rarely seem to have an explicit lower bound on the lengths of the papers. If they do, they will explicitly tell you so, and in those cases, the same society often publishes a journal for shorter papers.
If you proved an important result in a readable way on one page, almost no decent journal would ask you to add a bit of waffle to fit their criteria. So the question you should be asking is "which journals publish results of ---fill in--- importance/generality or on the topic of ---fill in---". Having said that, there are a few journals who particularly specialise on short papers, i.e. have an upper bound on length rather than a lower one. In addition to what has been suggested, you can have a look at the Bulletin of the LMS (the LMS also issues two other journals for longer papers). Also, the Bulletin of the Australian Mathematical Society promises short turnover times, which suggests that they like short papers. If you think that your paper is first class, then you can also consider the Annals of Mathematics, since they have a policy of encouraging short papers (by which they mean under 20 pages).
But as I say, I genuinly believe that no journal is going to turn down a paper because it is too short, unless this is their explicitly stated policy. So just choose a journal that you think is interested in your result.
On the other hand, unless you think that the brevity is a selling point of your paper, why don't you add a few examples to illustrate the interest or the usefulness of your result?
A: The American Mathematical Monthly publishes several short "Notes" in each issue, and I'm sure I've seen several that were only about a page.  As you would expect (being published by the MAA), many of these are mainly of pedagogical interest, but there are also some very interesting and nontrivial ones.
A: Here is an example of a 3 page paper in the Annals of Mathematics:
Hart Smith, An elementary proof of local solvability in two dimensions under condition $(\Psi )$, Annals Math, 136 (1992), 335--337.
So this is another piece of evidence that most journals have no objection to shortness in papers, even below 4 pages.  (This paper is not in my research area, but I know about it from knowing the author.)
