In the proof of Theorem 4.7 (Euclid’s proof that there are
infinitely many primes), the argument...
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In the proof of Theorem 4.7 (Euclid’s proof that there areinfinitely many primes), the argument uses calculation of a numberN. In each case below, suppose for the sake of demonstrating acontradiction, that the given list is the entire list of primenumbers. Calculate N and then factor N into primes to see that youdo get a contradiction.
(a) 2, 3, 5, 7, 11
(b) 2, 3, 5, 7, 11, 13, 17, 19
(c) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
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