Consider the quadratic congruence a x²+b x+c equiv 0 (mod p), where p is prime and a, b, and c are integers with p X a. a) Let p = 2. Determine which quadratic congruences (mod 2) have solutions. b) Let p be an odd prime and let d=b²-4 a c. Show that the congruence a x²+b x+c equiv 0 (mod p) is equivalent to the congruence y² equiv d (mod p), where y = 2ax + b. Conclude that if d equiv 0 (mod p), then there is exactly one solution x modulo p; if d is a quadratic residue of p, then there are two incongruent solutions; and if d is a quadratic nonresidue of p, then there are no solutions.