Interesting number theory and calculus theorems to prove

[UncertaintyAjay]

So, I like proving theorems in number theory and calculus. I'd like some interesting ones to prove. Recommendations?

 

[axmls]

Pick up Calculus by Spivak and work a bunch of problems from the end of the chapter. Very fun proofs to do.

 

[UncertaintyAjay]

Thanks, will do. Anything to do with number theory?

 

[axmls]

I don't have any particularly good problems or suggestions. Any decent number theory textbook will have plenty of proofs.

I recommend Spivak's for calculus because it's not quite so advanced as an analysis textbook, but it still contains problems in which you prove some very well known results (squeeze theorem being one of them off the top of my head).

 

[UncertaintyAjay]

Right, thanks.