1. The problem statement, all variables and given/known data Prove by contradiction that if b is an integer such that b does not divide k for every natural number k, then b=0. 2. Relevant equations 3. The attempt at a solution I know that proof by contradiction begins by assuming the false statement: If b is an integer such that b does not divide k for every kεℕ, then b≠0, which is equivalent to "there exists an integer b such that b does not divide k and b≠0, for every kεℕ. But I'm not sure how to proceed from here.