P is an odd prime When is 2p square modulo p P is an odd pri

Solution

for 2^p to be a square modulo p

when there are  there are exactly (p 1)/2 quadratic residues modulo p

Quadratic residues modulo p consists of the numbers 1^2,2^2,…,(p1)^2 by definition. But these p1 squares are pairwise congruent because of x^2(xp)^2mod p, So it suffices to take 1^2,2^2,…,(p12)^2.