Show that $\displaystyle n$ is prime iff $\displaystyle a^{n-1}$ ≡ $\displaystyle 1( \textrm{mod} n)$ for $\displaystyle 1 \leq a \leq n-1$.

=> Fermats little theorem.

<= (Wondering)

Perhaps show that $\displaystyle \phi(n) = n-1$ but if this is the case I would need a way to start.