Topics for an undergraduate exposition in number theory I have to give a 90~ minute exposition as a final assignment for my undergraduate number theory course and I'm looking for ideas on what to talk about. 
I've taken abstract algebra and complex analysis courses so it'd be great to use some machinery to prove a nice result. I was thinking something along the lines of the Gelfond-Schneider theorem but its proof is somewhat dry. 
Any ideas?
 A: I think you can get a great exposition out of the general subject of continued fractions. It is ideal for undergraduate number theory, fairly easy to pick up, absolutely fascinating, deep, and useful. It is not trivial. 
While you can find some good writing and proofs on the subject toward the end of any undergraduate textbook on number theory, you might want to pick up a book written by C. D. Olds titled "Continued Fractions" It is an old book from the Mathematical Association of America in the New Mathematical Library, but you will find it to be a great armchair read (nearby pencil and paper being handy).
I have several ideas on such an exposition. My thesis advisor actually listend to an exposition involving this book at an AMS meeting in San Francisco 1991 as evidenced by the copy he graciously gave me with that data inscribed inside the cover. The day I finally got around to reading it, I could not put it down till I hit the end, and I have been fascinated by the subject ever since. I have no question in my mind that you could easily entertain/amaze an undergraduate (or even post graduate) audience with an exposition on continued fractions.
