Show that if p is not a Fermat prime, then there is a such that

$\displaystyle

\left(\frac {a}{p}\right)=-1

$

and [a]_p is not a generator of $\displaystyle (\mathbb Z/p)^* $.

Here $\displaystyle

\left(\frac {2}{p}\right)=-1

$

is legendre symbol.