I would like some help with this question:
Q: x^2+x+1=0 (mod 13)
I can't factorise the LHS as it stands, so I changed the 0 to 13, rearrange to give:
x^2+x-12=0 (mod 13)
(x+4)(x-3)=0 (mod 13)
x=-4 or 3 (mod 13)
Does my method work or have I gone wrong somewhere? Pointers would be greatly appreciated.