Euler's phi function

Euler's phi function $\phi$(n) is the size of Z^*_n = { : gcd(a,n) = 1}, the multiplicative group mod n. $\phi$(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 .