TEST BANK FOR Mathematical analysis 2nd Edition By Apostol Converted

1.1 Prove that there is no largest prime. Proof : Suppose p is the largest prime. Then p!+1 is NOT a prime. So, there exists a prime q such that q |p! + 1 ) q |1 which is impossible. So, there is no largest prime. Remark: There are many and many proofs about it. The proof that we give comes from Archimedes 287-212 B. C. In addition, Euler Leonhard (1707-1783) find another method to show it. The method is important since it develops to study the theory of numbers by analytic method. The r...