Math projects

<p>So does anybody have ideas for good/advanced math projects? I'm interested in number theory or calculus. I went to PROMYS this summer, so I get the gist of number theory projects.<br>
I was thinking a project on r-gonal numbers, but I don't know of a specific question I could answer.<br>
Maybe Diophantine equations, but again, I can't think of anything specific.<br>
I would really appreciate any suggestions
Thanks in advance!</p>