1. ## primitive root

For which prime p does the congruence (x^2 + 4x + 5) mod p =0 have

2. Originally Posted by fyw891105
For which prime p does the congruence (x^2 + 4x + 5) mod p =0 have
1) if p = 2 then $\displaystyle x^2+4x+5=x^2+1=(x+1)^2\!\!\!\pmod 2$ and we have a double root;
2) If p > 2 then the equation has a solution iff the quadratic's determinant is a square modulo p, i.e. $\displaystyle \Delta=16-20=-4$ is a square modulo p $\displaystyle \Longleftrightarrow -1$ is a square modulo p.