Here is my attempt
When we raise both sides to the power (p-1)/2, we get
x^(p-1)= -1^[(p-1)/2](modp)
Looking at p=3(mod4), the possible values of p are
{3, 7, 11, 19, 23, 31...}.
Putting these values of p into (p-1)/2 we get odd integers.
{1, 3, 5, 9, 11, 15...}.
So we have
x^(p-1) =...