Theorem. If $\displaystyle p$ is a prime and $\displaystyle (a,p)=1$, then the congruence $\displaystyle x^n$ $\displaystyle \equiv$$\displaystyle a (mod p)$ has $\displaystyle (n, p-1)$ solutions or no solution according as

$\displaystyle a^{(p-1)/(n,p-1)} \equiv 1 (mod p)$

or not.

Can someone explain what this means linguistically? I don't understand what "according as [...] or not" means.