$($a$)$ Let $p$ be a large prime number such that $N=2p+1$ is also prime. What are the possible values of the order of an element modN $?($Recall that the order of an element mod $N$ must be a factor of $(N).$

$($b$)$ Eve is eavesdropping on Alice and Bob performing Diffie$-$Hellman key exchange. They are using the modulus $N$ from part $($a$),$ but she has the additional ability to choose the $g1$ that they will use as a generator. What order does she want $g$ to have to make the discrete log problem as easy as possible?