I wanted to publish a research paper which has less relevant stuff compacted and would be more focused on important and relevant items.
Also, I have failed to find a guide to publish small compact research papers.
Yes, if your ideas can be expressed concisely enough. For example if you were to find a counterexample to the Beal Conjecture, then you can write two paragraphs and be done. Watson and Crick's 1953 paper describing the structure of DNA was one page long, and won the Nobel Prize. Some other examples of very short papers (admittedly, some of these are jokes) are here.
My favorite short paper, which like Nash's in another answer is from the 1950s, is as follows:
I do have a hard time seeing how it would be published these days, but clearly very short papers have been acceptable in the past.
John Nash published a paper entitled Equilibrium Points in n-Person Games. The paper is one page long. But it's John Nash, and it was in 1950. It was the beginning of a whole new field (game theory), and the man was a genius. (Credit to MathOverflow.)
It is entirely up to the journal or conference.
Most venues have page limits but I have never heard of a minimum. I've seen some really short papers in math journals. Submit it to a venue that you think it would fit in!
This will often depend on the journal in question. In my field, "Brief Reports" and "Letters" are often quite short, and sometimes less than a single page, highlighting a particular case, a minor point of interest, etc.
A paper should say a little bit about the significance of the result and prior research. In mathematics, the definitions need to be quoted or given. Doing that in one page, along with the result, could be tricky.
But it is definitely possible.