Originally Posted by

**twells1303** yes,

but what you are writing helps me to look at solutions of the form x^2 + b =0 (mod p), but not the form I want x^2 + bx + c = 0 (mod p).

I know the stuff you are saying...what I need is an algorithm that efficiently checks for solutions and also would like to know if there are some conditions that could be put on b,c, and p that would guarantee a solution to this.

It doesn't seem like you are addressing my question, but really adressing a much simpler question using quadratic residue theory.