For which prime numbers p does the congruence $x^2+x+1\equiv0$ mod p have solutions?
I am new to the topic of quadratic reciprocity and I know how to answer this question had it been for which prime numbers p does the congruence $x^2\equiv-6$ mod p have solutions?
Can I perhaps split the congruence into two parts, solve them individually and then combine solutions?
Thanks in advance.