Is there a simple way to prove that ɸ(p) = p - 1
I would appreciate any suggestions
In the specific case you bring up n is a prime (from $ɸ(p) = p - 1$). Since every natural number less then p is relatively prime to p all you have to do is count the natural numbers less then p to get your $\phi(p)$, which happens to be $p-1$.
The definition I have is; $\phi(n)=$the number of integers a that satisfy $0\leq a<n$ and $gcd(a,n)=1$