08401/Homework Assignment 5

Contents 
Reading
Read chapters 16 and 17 (to page 306) of Gallian's book (6th edition) three times:
 First time as if you were reading a novel  quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
 Second time like you were studying for an exam on the subject  slowly and not skipping anything, verifying every little detail.
 And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.
Doing
Solve problems S20, 22, 24, S27, S31, 32, 38, S39, 40, S45, 49 in Chapter 16 of Gallian's book (6th edition) and problems 2, S4, 5 in Chapter 17 of the same book, but submit only the solutions of the problems marked with the letter "S".
Due Date
This assignment is due in class on Wednesday February 13, 2008.
The notes below are by the students and for the students. Hopefully they are useful, but they come with no guarantee of any kind.
Corresponding Questions for Gallian's 5th Edition
Chapter 16  S20, 22, 24, S27, S31, 32, 38, S39, 40
S45: Let F be a field. Show that there exists a,b in F with property (x^2 + x + 1) divides (x^43 + ax + b)
49: Show that 1 is the only solution of x^25  1 = 0 in Z/37
Chapter 17  2, S4, 5
solution to selected problems [1]