The other answers don't seem to be taking into account that the OP is a 13-year-old junior high school student whose work was presented in a school science fair. I think that treating the OP as a "very junior researcher" is a bit unrealistic and also may place too large a burden on him. Every week on this site we see adult researchers placed in great distress and turmoil by issues of plagiarism and academic priority. These are not easy matters to resolve, and they place a high level of burden on the individual academics because academia is essentially self-policing. A junior high school student is not a professional academic, almost certainly has none of the procedural training and academic contacts that a professional academic would, and therefore does not have an ethical obligation to respond as a professional academic would.
The first thing I want to say is that I don't think the OP is obligated in any way to respond to this incident, as other answers seem to imply that he is. He can do so if he wants to, but if so I would recommend getting help from someone else.
Another important issue here is that the OP doesn't even understand the mechanism by which his work was made public. To me this seems to suggest that if he wants to pursue it, he should begin at the level of his own school. Presumably there is some teacher / faculty advisor involved in the science fair. I would contact them or have a parent contact them. This really is (or could be) an issue in itself: a school should not be releasing a student's work
on the internet without the student's permission or awareness.
If the OP doesn't have a clear understanding of how his work got made public in the first place, then unfortunately it seems to me that he is in an unusually poor position to press a case of academic priority. He could contact the editors of the journal, submit all the evidence of his work along with the chronology, and the authors could respond simply by saying "We don't know anything about this. Actually our work was done [at some earlier date]. As far as we can tell, some kid stole our work for a junior high school science fair. What should we do about this?" and I don't see what the editors of the journal could plausibly do to resolve the situation.
This sounds bad, but let me make a few more comments:
In my experience, outright theft of work by serious academic mathematicians is extremely rare. One of the reasons for this is that the worldwide mathematical research community is relatively close-knit. If you're working in area X, then you probably trained at a certain set of universities and have affiliation, direct or indirect, with very serious senior reputable workers in area X. Having a senior worker in area X think you've stolen someone else's work is a penalty far beyond the reward of publishing the work, in most cases (contrary to what popular culture may lead one to believe, the vast majority of contemporary mathematicians build their reputation on a steadily accumulating body of work, not one miraculous theorem). Most areas of modern mathematics are so technically intensive that there are very few to no real outsiders contributing. However, a real outsider -- e.g. someone who has had no face-to-face interaction with any university faculty member -- who does do significant mathematical work is unfortunately in a much worse position.
As a consequence of the above, when a brilliant 13-year-old's work gets stolen, it's very likely that it gets stolen by people who are not serious academic mathematicians, and it gets published in a journal which is not really serious and reputable. If this is the case, then the stakes may be too low to justify the time and effort of trying to resolve the situation. I am a professional mathematician, and if someone republished my work as their own (this has never happened to me) I would probably be upset and try something to fix it, but there are some journals where I would give up rather quickly.
So as a summary answer to the first question:
Firstly, what can I do about this,
Take it slow, starting in your own home and at your school. See if you can get some help with pursuing your claim. If the claim turns out to be more trouble than it's worth to press: you can choose not to press it. Try to gain a clear understanding of how this happened, so that it will not happen again.
As to your second question:
secondly, it had never occurred to me that my work may be of the quality to publish, so once I do get this situation sorted out, could I possibly think of publishing my results myself?
As I said in a comment, I would advise almost any junior high school student not to think about publishing their mathematical work. Note that I did not say to stop or slow down in the learning and doing of mathematics in any way. In fact, the point is that the publication process is something that is done by professionals largely for reasons of professional exigency and not because it is pleasant or educational in its own right. When I work with PhD students to try to get their first paper published, there comes a point where they realize that the amount of effort to do so (even after all the theorems are proven) is something like 2-10 times as much as they expected. It used to be that math PhD students could mostly just concentrate on the math and not worry about publishing anything until after they got their PhD, but unfortunately those days are largely gone. (In my department, one of the required features of the postdoctoral application is the publication list. An empty list is surmountable, but it certainly does not augur well.) Moreover, undergraduates who do summer math research are now being much more pressured to write up their results -- even when they are not really significant, and even when they were largely put up to the results by their faculty mentors -- and this is very worrisome. The OP is 13 years old. It is widely recognized that children of this age should not be working: the Fair Labor Standards Act says that in the US one must be 14 to legally work at all. This does not apply to mathematical research, and it is certainly legal for the OP to pursue publication, but it is almost as worryingly too-soon for the OP to try to pursue this as if he had a serious, difficult job.
Let me say finally that I looked at the OP's internet profile, and it is clear that he is remarkably talented and precocious. I highly encourage him to continue his study of mathematics, so long as his motivations for doing so are his own. Based on what I've seen of the OP, I do not discount the possibility that he has already done work that could get published in a reputable journal (although that is highly unusual for someone of his age). What I would say to him instead is: keep doing what you're doing. Think about where you are now compared to where you were a few years ago and try to imagine where you'll be a few years in the future (while still in high school!). If you're still doing math 3,5,10 years from now, what would your future self advise your 13-year-old self to do? Is the work that you're doing now going to be a shadow of your later work?
Look e.g. at Terence Tao, who is arguably the world's leading mathematical-prodigy-grown up. According to wikipedia, he published "his first assistant paper" at the age of 15. But I don't know what that means, and I can't find the paper. His first that is catalogued in the standard places was published in 1996, the same year he got his PhD, at the "advanced age" of 21.
Note also that you should not hesitate to interact with the mathematical community, as you have been. I see that you have a blog. This gives you a great place to post your work, talk about it there, and get feedback from others.
The very last thing I'll say on the matter is that you said the project in question is on elliptic curves over finite fields. In fact elliptic curves are
my leading research interest at the moment. So I would be happy to see your work and give you some feedback on it. Of course you should not send the work to me if (i) you are not ready or (ii) have any concerns about it being stolen by me! For the latter, I might recommend putting it on your blog first and then sending me a link to the blog. But I am aware of some contemporary research on this topic and would be happy to steer you in a good direction if I can.
