1. Find all solutions x (with 0 ≤ x ≤ 96) to the congruence 13x^385 + 73x^304 + x^290 + 10x^193 + 24x^112 + 70x + 76 ≡ 0 (mod 97) I was able to reduce, using Fermat's Little Theorem, to get 97x^16 + x^2 + 93x + 76 ≡ 0 (mod 97), but I don't know how to proceed from there. Is there another trick I can use? 2. http://imgur.com/a/DUyHC RR denotes two adjacent quadratic residues, while NN denotes two adjacent quadratic non-residues. RN is a residue followed by a non-residue, and NR is a non-residue followed by a residue. I tried to solve the problems by adding and subtracting the four expressions given in part b but I haven't made any progress. Thanks for the help!