1. [4 marks] Number theory. (a) [1 mark] Prove that V71 6 Z, gcd(7n + 1, 1511 + 2) = 1. HINT: Use SOme of the facts from Warksheets 67 for a very short proof. (b) [3 marks] Prove that there exists exactly one prime of the form n3 1. (When we say that a number p has \"the form n3 1,\" we mean that there exists some integer n such that p = n3 1.) Before you start your proof, rst express the statement symbolically. HINT: n3 1 is equal to the product of two other polynomials in n