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 Theorem 1.42 from page 19 of our text.
3. Hopefully, you
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 is also of the form 6m + 1.
(b) Each integer of the form
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 the rst is divisible by 52 , the second is divisible by 3
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 page 34.
4. Prove the following: There are arbitrarily
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 Euclidean Algorithm to nd the GCD and then reverse the steps to
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 presentation, determine (77).
(b) Use the information from
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 with playing with numbers and looking for patterns. Fi
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 divides 248 1 using congruences. Then nd some other prime fa
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
results, come up with a conjecture. You do not need to pro
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 requested in Exercise 1.56 from page 23 of our text. Also pro