a. Bzout's identity states that for positive integers a and b, there always exist integers m and n such that am + bn = gcd(a, b). Also, recall that a = b (mod n) means that there exists an integer such that a-b=ln. As you know, this is called modular equivalence or modular congruence. -1 Recall that (if it exists) the multiplicative inverse of p modulo q, is defined to be the unique number p- such that p p 1 (mod q). E i. Apply the definition of modular equivalence and write down what p p 1 (mod g) means. 1 mark. ii. Rearrange what you get and apply Bzout's identity to conclude that if gcd (p, q) = 1 then p exists (modulo q). 2 marks. b. The Division algorithm tells us that, given positive numbers a and b, with a b, there always exist integers q and r, with 0r