Let a and b be integers. (a) Re-write the definition of gcd(a, b) in terms of the partial order "divides", |, from the previous question. (b) Fix an integer d. Show that if (r, s) is a pair of integers such that d = ar+bs then (r+kb, ska) is another such pair. (c) If a and b are nonzero and there exists a pair (r, s) of integers such that 1 = ar + bs show that gcd(a, b) = 1. (d) Is the same true if d = ar + bs? Namely, can we conclude that gcd(a, b) = d? (e) Suppose gcd(a, b) = 1 and (r, s) is a pair of integers such that 1 = ar + bs. Show gcd(a, s) = gcd(r, b) = gcd(r, s) = 1.