Hey everyone, couple problems I am stuck on.

1. Let $\displaystyle p$ be an odd prime and $\displaystyle p \equiv 3 \ mod \ 8$. Show

$\displaystyle 2^{\frac{p-1}{2}} \cdot (p-1)! \equiv 1 \ mod \ p$

2. $\displaystyle a$ is an integer such that $\displaystyle gcd(a,35)=1$, show that

$\displaystyle a^{12} \equiv 1 \ mod \ 35$

and then deduce there exists no primitive roots modulo 35.

I don't know how to do question 1 so need a lot of help for this one.

For question 2, a must be coprime to 35, so is it good enough to just say $\displaystyle a=2$ and show $\displaystyle 2^{12} \equiv 1 \ mod \ 35$ ?

And how do I do the second part of q2?

Thanks all for your help.