Need to know how to do this sort of discrete maths questions.?

Guys just started self-learning discrete maths, and its really troubling me as its really different from high-school continuous maths that I learnt. So here's some kind of questions that I need help with: Q1. If a is congruent to b mod(n) and c is congruent to d mod (n) then ac is congruent to bd mod (n). Using this and 9^2 = 4 mod (7) as a facts, find a number r belong to {0,1,2,3,4,5,6} such that 9^91 is congruent to r mod(7). Explain the reasoning. - Ok for this I've been trying to find a powers of 9^n, like 9^1, 9^2, 9^4 and so on.. but it saids I shouldn't need to have large numbers.. Q2. Prove the following statement by contradiction: If x,y belong to real numbers, with x>0 and y>0, then (x+y)^2 ≠ x^2 + y^2. Q3. The numbers 271 and 327 each lies in one of the elements [0], [1], [2], [3] of Z(4) - identify which ones they lie in, giving a reason in each case. Then, find all the solutions of [x] of the equation [3] [x] = [4] in Z(5). I'm getting the hang of the questions sets and subsets questions of Universe kind of stuff.. but proving & disproving part of it it's making me a headache.