I will answer your question in a somewhat sideways manner: I think anyone who is trying to write a math research paper who does not already have a PhD in mathematics or a closely related field should do so in close consultation with an adviser who does have such a PhD. It is not practical to learn all the standards of journals and publishing on your own. Virtually every undergraduate is also in the following situation: their own perspective on mathematics is not yet mature, and thus if they submit a paper to a research journal they will be submitting their work to an audience with far more experience and background knowledge. (A few truly brilliant undergraduates do work up to the standards of other mature, professional mathematicians, but even for them the work is probably much less than what they will be capable of later on. I can't think of a single instance of a professional mathematician whose undergraduate work was in the same league as their later research.)
In fact -- and I don't mean to be discouraging by saying this -- most research done by undergraduates is not of a publishable quality. This does not mean that undergraduates should not engage in research -- I think it is very valuable and enjoyable for them to do so (if anyone cares: I did research as an undergraduate, had a blast doing it, and did not try to publish it) -- but only that formal publication should probably be a goal for later in one's career than that, especially nowadays when it is so easy to put your work on the web.
In particular, you write
a particular statement/fact is commonly known to all and its discoverer/inventor is not known, and that there exists no research paper that introduced the concept but there do exist various books/websites that discuss the very concepts and a few derivatives of the concept?
Honestly, this sounds unlikely to me. The vast majority of mathematical topics that are discussed in books are also discussed in research papers (maybe it is somewhat different in recreational mathematics, but even there I imagine it's still mostly true). How do you know that no research paper treats the concept in question? Searching the mathematical literature is itself a skill that takes both general experience and specific expertise in the subfield you're searching in: as a research mathematician it is common enough for me to come across a mathematical concept, try to find it in the literature, and only find it several weeks or months later when I have become more familiar with the local terminology and standard results. Similarly, most mathematical concepts are traceable to a specific discoverer/inventor, although admittedly the generic mathematician does not feel as honorbound to track down primary sources as academics in most other fields (in my opinion this is a rare "character flaw" of the generic mathematician!).
Even if you have done all the mathematical research yourself, consulting an experienced adviser on how to write up and submit your work could save you a lot of time and headache. Some journals/editors/referees are relatively supportive of authors writing their first paper (everyone who has published a paper was in that situation at one time!), but if your paper is, or looks to be, below the level of papers they want to publish, it will probably get bounced back to you with little constructive criticism. An adviser can be much more kind...