1. (a) (6 points) Consider the top-level and recursive calls made by the Extended Euclidean Algorithm in computing gcd(19, 45). Make a table of the pairs of arguments (a, b) in all these calls, and the pair (r,y) of integers found by the algorithm such that 1 pair of arguments (0, 1) if you like.) = xa + yb for each such pair (a, b). (You may skip the (b) (2 points) Recall that two integers m and n are relatively prime if and only if gcd(m, n) = 1. How many elements of the set S = {n N|0