Assignment:
Q1. If g is a primitive root of p, show that two consecutive powers of g have consecutive least residues. That is, show that there exists k such that g^(k+1)=g^k+1(mod p) (Fibonacci primitive root)
Q2. Show that if p=12k+1 for somek , then (3/p)=1
Q3. Show that if a is aquadratic residue (mod p) and ab=1(mod p) then b is a quadratic residue (mod p)
Q4. Suppose that p=1+4a, where p and q are odd primes. show that (a/p)=(a/q).
Provide complete and step by step solution for the question and show calculations and use formulas.