I'm a grade 12 student interested in Number Theory, Graph Theory and Combinatorics and I am currently looking for ideas for an original research project/paper in mathematics. I was hoping that someone could recommend me some areas or topics of research which are challenging yet do not exceed my capabilities.
I have done lots of competitive (Olympiad) level mathematics, especially number theory, combinatorics and inequalities. Geometry is a bit weak though. I've taken basic single variable calculus courses as well. I don't know much abstract algebra (if anyone can recommend some good places to start learning, that'd be great!) or statistics/probability. I can program in python and work in LaTeX.
I really appreciate all help! Thanks!