h2 115A - MAT 115A University of California Fall 2010...

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MAT 115A University of California Fall 2010 Homework 2 due October 13, 2010 1. Rosen 3.1 #4, pg. 74 Use the sieve of Eratosthenes or Sage to find all primes less than 200. 2. Rosen 3.1 #5, pg. 74 Find all primes that are the difference of the fourth powers of two integers. 3. Rosen 3.1 #11, pg. 74 Let Q n = p 1 p 2 ··· p n +1, where p 1 ,p 2 ,...,p n are the n smallest primes. Determine the smallest prime factor of Q n for n 6. Do you think that Q n is prime infinitely often? ( Note: This is an unresolved question.) 4. Rosen 3.2 #3, pg. 86 Show that there are no “prime triplets”, that is, primes p , p + 2, and p + 4, other than 3,5, and 7. 5. Rosen 3.2 #21, pg. 87 (challenging!!) A prime power is an integer of the form
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This note was uploaded on 10/23/2010 for the course MATH math 115A taught by Professor Anne during the Spring '10 term at UC Davis.

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