\f(8) Find all primes p for which the equation has a solution (i) X3 - 11 =0 mod p, (ini) X2 -6=0 mod p, (1i) x2 - 10 =0 mod p (iv) X2 - 14=0 mod p.(10) Prove that the congruence X2 +3=0 mod n has no solutions when n = 72 . 192 . 23, and has eight solutions when n = 72 . 192 . 31.(12) Let p be an odd i}rim;-: number, and a,b,c & be such that p{ a. Denote by D = b* dac the discriminant of the quadratic polynomial f(X) = aX? + bX + c. Prove for the equation flX)=0 modp that (i) there are no solutions if pt D and (f) ==1; (it) there is one solution when p| D; (iii) there are two solutions when pt D and (;':) =1