Homework Assignments for
Dr. Sadun's M328K Sections, Spring 2003
Last updated April 16

There will be homework assigned every week, due on Wednesdays, every week except those weeks with exams.

Homework #1: (due January 22)
1.1 p.14: 4, 8, 12, 24, 26.
1.2 p.22: 2, 8, 12, 14, 24.

Recommended additional problems from the textbook
(you don't have to turn these in)
1.1 p.14: 1, 2, 3, 7, 25.
1.2 p.22: 4, 5, 11, 22, 27, 29, 33.

Homework #2: (due January 29)
1.4 p34: 6, 8, 12, 35
3.1 p76: 4, 16,
3.2 p84: 2, 8, 10

Homework #3: (due February 5)
3.2 p84: 14, 24
3.3 p94: 2, 4, 10
3.4 p104: 2, 10, 30, 46, 66
3.5 p117: 2, 4

Homework #4: (due February 12)

3.6: 2, 6, 8
4.1: 2, 8, 10, 22, 28, 34
4.2: 2, 6, 10

Homework #5:
There is no written homework due February 19, due to the exam on February 21.  However, I recommend that you  work the following problems on your own:

4.2: 13, 14, 15, 16
4.3: 1, 3, 7, 9, 12, 15, 33

Homework #6: (due February 28, because of the school closure on February 26)

4.3: 4, 8
4.4: 2, 4, 10

Homework #7: (due March 7)

4.4: 6
4.5: 2
5.1: 2,3,4, 20, 22, 24, 25, 26

Homework #8: (due Wednesday, March 19)

(The following problem was assigned in class but wasn't previously listed.  If you have not already turned this in, do so now):
Determine, with complete proof, which Fibonacci numbers are divisible by 4.

A year is chosen at random from 2001 through 4800. That is, each of those years has a 1/2800 chance of
being chosen.  Prove that the probability of Christmas falling on Sunday in the chosen year is NOT 1/7.  (Easter, however, has a 100% probability of landing on Sunday). [Note that you do not have to calculate the probability that Christmas falls on a Sunday -- you just have to show that it can't be 1/7.]

5.2: 2 (skipping (a), (b) and (c)), 6, 10

Homework #9: (due March 26)

5.5: 6, 8, 12, 14, 18, 20
6.1: 2, 4, 6, 10

Homework #10: (due April 2)

Give a careful and complete proof of the following assertion:
"(n-1)! is congruent to:
-1 (mod n) if n is prime,
0 (mod n) if n is composite and greater than 4, and
2 (mod n) if n=4. "

6.1: 14,18, 20,  22, 24, 40
6.2: 2, 8

Homework #11 (due April 23)

7.1: 2, 4, 6
8.1: 2, 4, 10, 12, 14, 16

Homework #12 (due May 2)

1)  solve the CRT problem for ALL values of a and b:
x = a (mod 123)
x = b (mod 25)

2) A message is encoded with the coding

x => x^(125)  (mod 8633)

Find the decoding.

3) Give a careful proof of the Chinese Remainder Theorem for 2 moduli, namely:

If (m1,m2)=1, then there is a unique solution, modulo (m1 m2) to the system of equations

x = a (mod m1)
x = b (mod m2)