In this question, we work through euclid's proof that there are infinitely many primes. sup- pose, by way of contradiction, that there are finitely many primes. then we can list all of them: a, b, d. now let n = (a x bx cx..x d) +1. there are two possibilities. either n is prime or n is composite. (a) case i: suppose n is prime. complete the proof. (b) case ii: suppose n is composite. explain why n must have a prime divisor. call the prime divisor g. explain why g must be in the original list a, b, d. assume, without loss of generality, that g = a. clearly a divides (ax bx d) since a also divides n, a must divide the difference between n and (ax bxcx..x d). why?