Quadratic Reciprocity

[bigp0ppa1046]

Determing whether the following has a solution (the modulo is prime):

x^2-64x+943 is congruent to 0 (mod 3011)

Our book has nothing about this, how do I even start? Do I factor? Help please.

 

[Denis]

hint: 23,41

 

[bigp0ppa1046]

well i see that i get x=23 and 41 when i factor but what does that tell me? where do i go from there?