These are problems based on quadratic residues.I hope you are familiar with the legendre symbol. For reference, if p is an odd prime...

(a) Compute

(b) Since (31,3) = 1, compute

(c) ( ) is same as ( ). Again we have (2,41) = 1. Therefore compute

(d)This one is interesting. You have to transform this quadratic congruence to linear by completing the squares and then find the quadratic residue