TEST BANK FOR Mathematical Analysis 2nd Edition By Apostol
Harvard University
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Examen
TEST BANK FOR Mathematical Analysis 2nd Edition By Apostol
Exam (elaborations) TEST BANK FOR Mathematical Analysis 2nd Edition By Apostol 
The Real And Complex Number Systems 
Integers 
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) fin...