First, I'm in need of a topic to write a paper about as part of my degree requirements. The paper is supposed to be 10-15 pages. (I only mention this because it limits the scope of the paper and thus the topic.) 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.