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I took a course in number theory last semester and really enjoyed it, so I'm really looking for something in that area, although I do enjoy Abstract Algebra as well.

So far, I've tried p-adic numbers and Gaussian Integers.

There didn't seem to be enough about Gaussian integers that was accessible to write a paper about, also I'm not a fan of Complex Analysis.

P-adic numbers seems very promising, but when reading about them, I didn't have that ah-hah! moment.

I've spent a few hours on google already, and intend to spend a few more, I would just be remiss if I didn't ask on here.

I'm open to any suggestions, links, or otherwise.

EDIT: Cryptography might be another thing I try. We spent a lot of time on it last semester, and it seems like it has its roots in Number/Group Theory. And being an application, I feel it would make a more readable paper.