What parts of number theory does the RSA algorithm use?

It is said that the RSA algorithm uses number theory. What parts of number theory does it use?
I know it uses modular arithmetic and Euler's totient theorem and function. Is that all?

-

In fact, RSA as practiced (that is, PKCS#1) does not even use Euler's phi function for $d\equiv e^{-1}\pmod {\phi(N)}$; but rather uses the (less frightening) Least Common Multiple: $d\equiv e^{-1}\pmod {\operatorname{LCM}(p-1,q-1)}$, because that's the necessary and sufficient condition for a working $d$ (when all the factors of $N$ are distinct). – fgrieu Dec 23 '13 at 12:24