Problem 2 (12 marks) For all x, y E Z with y > 1: (a) Prove that if god( x, y) = 1 then there is at least onew E [0, y) n N such that wx =(y) 1. (Hint: Use Bezout's identity) (4 marks) (b) Prove that if god(x, y) = 1 and y |kx then y |k. (4 marks) (c) Prove that if god( x, y) = 1 then there is at most onew E [0,y ) n N such that wx = (y) 1. (4 marks)