Question: Finish the proof of Theorem by proving that if a, b and c are as in the proof, then c | b.
Theorem: Writing a Greatest Common Divisor as a Linear Combination
For all integers a and b, not both zero, if d = gcd(a, b), then there exist integers s and t such that as + bt = d. In particular, if a and b are relatively prime, then there are integers s and t with as +bt = 1.