Collected Homework Week 5
MATH 278: Number Theory
Due February 14, 2011 at 4:00pm
(Happy Valentines Day!)
Name (Print):
1. Write a proof of Theorem 1.39 from page 19 of our text.
2. Write a proof of T
Collected Homework Week 9
MATH 278: Number Theory
Due: March 21, 2011 at 4:00pm
Name (Print):
Extension: March 23, 2011 at 10:00am
1. Prove the following statements:
(a) Any prime of the form 3n + 1 i
Collected Homework Week 13
MATH 278: Number Theory
Due: April 20, 2011 at 4:00pm
Name (Print):
Extension: April 27, 2011 at 4:00pm
1. Chinese Remainders
(a) Find three consecutive numbers such that th
Collected Homework Week 8
MATH 278: Number Theory
Due March 14, 2011 at 4:00pm
Name (Print):
1. Write a proof of Theorem 2.18 from page 33 of our text.
2. Exercise 2.22 on page 34.
3. Exercise 2.23 on
Collected Homework Week 4
MATH 278: Number Theory
Due February 7, 2011 at 4:00pm
Name (Print):
1. Write a proof of Theorem 1.32 from page 18 of our text.
2. For each of the following, use the Euclidea
Collected Homework Week 15
MATH 278: Number Theory
Due: May 3, 2011 at 4:00pm
Name (Print):
Extension: May 4, 2011 at 4:00pm
1. The Euler- Function
(a) Using the results from Jena and Xiaochuangs pres
Collected Homework Week 3
MATH 278: Number Theory
Due January 31, 2011 at 4:00pm
Name (Print):
1. (This was an exercise on the rst groupwork sheet.) As we have discussed, number theory has a lot to
do
Collected Homework Week 10
MATH 278: Number Theory
Due: March 28, 2011 at 4:00pm
Name (Print):
1. Prove the following statements:
(a) Show that 53103 + 10353 is divisible by 39.
(b) Show that 97 divid
Collected Homework Week 11
MATH 278: Number Theory
Due: April 6, 2011 at 4:00pm
Name (Print):
1. Lets experiment a bit! Determine the residue of (n 1)! modulo n for n = 3 through n = 12. From your
res
Collected Homework Week 6
MATH 278: Number Theory
Due February 21, 2011 at 4:00pm
Name (Print):
1. Write a proof of Theorem 1.55 from page 22 of our text.
2. Write a clear, complete denition as reques