I have a question. I am interested in finding the solution to congruences of the form:

x^2 + ax + b=0 (mod p) with p a large prime. I am interested in an algoirthm for finding solutions to this that is more efficient then checking all of the numbers 1,....,p-1. Also, I would like to know what conditions can be put on a, b and p to guarantee the existence of an integer solution to this congruence.

Any ideas?