Question

IF P AND q are odd primes, then

Answer 1

Answer:

Prove that if p and q = 2p + 1 are both odd primes then −4 is a primitive root of q. ... If ordq(−4) = 1 then (−4)1 ≡ 1 mod q so then q | −5 which means q = 5 but then 2p +1=5 and so p = 2 which it can't be since it's an odd prime. If ordq(−4) = 2 then (−4)2 ≡ 1 mod q so then q | 15 which means q = 5 or q = 3.