several other answers have mentioned submitting to arxiv which is indeed a sometimes prestigious and elite site occasionally containing some work/papers submitted by undergraduates. you appear to be affiliated with a university. fyi this is a semiofficial requirement of arxiv submissions, sometimes [apparently] judged by your ".edu" on your email address.
if you are not "university affiliated", arxiv can be harder to submit to. it requires the support of one of the [unlisted] moderators.
generally it seems [speaking from experience] their acceptance policy is rather opaque and occasionally verging on arbitrary for borderline cases. if you submit a paper and you're in, great, but if its not accepted based on the sometimes sketchy criteria [which seems not to be published or clearly articulated anywhere on the site], you wont necessarily have a clear path to fix that. in other words the structure is not at all set up to encourage/help/coax borderline cases to make it in [it is somewhat similar to stackexchange in this way, but also maybe scientific journal submissions].
so fyi, a relatively new alternative that was recently created specifically/partially in protest of arxiv's opaque and not-fully-open submission policies is vixra which seems to be stable and attracting a healthy dose of submissions. more details on their policy and contrast to arxiv can be found on the page "why vixra". quoting from that:
Vixra is also an experiment to see what kind of scientific work is being excluded by the arXiv. But most of all it is a serious and permanent e-print archive for scientific work. Unlike arXiv.org it is truly open to scientists from all walks of life. You can support this project by submitting your articles.
as to another reasonable suggestion by JF in the other answer:
Alternatively, you could just post it as a question here, asking if the result was previously known, or if anybody could point you to a good survey paper on the problem. You'd have a time stamp from the post time, so you wouldn't have to worry about that. If you got an encouraging response here (i.e. that it was not currently known), then you could consider how to proceed from there. If on the other hand, it was already known, or there was a flaw, then it wouldn't really matter.
again, personal experience, I tried this to some degree here with some of my own ideas & had some degree of success, but it was highly variable and unpredictable. however, dont really recommend the above in this forum (TCS.se) for several reasons. if your question is upvoted beyond a certain threshold, it is likely to stay here forever unmolested.
however in a borderline case (which frankly is the likely case here for an undergraduate attempting to accomplish a genuine research advance), the question could easily be closed and deleted, and on stackexchange, these questions are totally vaporized without trace (all comments, all answers, etc, everything is completely wiped out as if the question had never appeared in the 1st place) see why and how are some posts are deleted. surely not what you intended, so much for "a time stamp from the post time, so you dont have to worry about that"...
another less severe but still problematic case here [from the POV of the originator] are questions that end up getting heavily edited via the collaborative editing, and get pushed away/drift significantly from your original intentions/meaning. see why can people edit my posts, how does editing work.
you may have better luck starting out in cs.stackexchange. occasionally very advanced questions there get migrated to this forum.