Euler's phi function (n) is the size of *Z*^{*}_{n} = {
: gcd(a,n) = 1}, the multiplicative group mod n.
(p) = p-1 if p is prime.

**Euler's Theorem**

For any integer n > 1, (mod n) for all .

**Fermat's Theorem**

If p is prime, then (mod p) for all .