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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.
 Spring '10
 anne
 Number Theory

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