781hw1 - f x = 5 x 2 Test a few examples and try to come up...

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18.781, Fall 2007 Problem Set 1 Due: FRIDAY, September 14 1. Complete the following problems from Niven-Zuckerman-Montgomery (henceforth NZM): NZM 1.2: 2, 3 (part a and c only), 9, 11, 13, 34, 36, 46, 50 NZM 1.3: 5, 10, 26, 27, 31, 33, 41, 48 2. Using the PARI program written in class as an example, use a computer program to test for when a given polynomial f ( x ) represents infinitely many primes. That is, are there infinitely many x for which f ( x ) is prime? (Our in-class example showed this to be true when
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Unformatted text preview: f ( x ) = 5 x + 2.) Test a few examples and try to come up with conditions on f as to when this can happen. When it happens, can you determine how fast this quantity is approaching infinity? Does the growth condition depend on f ? Give a print-out of your computer investigations and then add com-ments according to your conclusions about the above questions or other interesting ideas that occurred in the course of your experimentation....
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