March+1

Exercise

a) Find all the quadratic residues modulo 19. b) How many quadratic residues are there modulo 31? c) Show that the congruence math (x^2+1)(x^2+2)(x^2-2)\equiv 0 \mod p math has a solution modulo any prime.

Question

Let math p=2^n+1 math be a prime (n>0).

Show that a is a quadratic non-residue modulo p if and only if a is a primitive root modulo p.