Announcements 1/29/2012
1. As announced in a previous e-mail, the due date for the first homework has been changed to
Tuesday Feb. 5.
2. In homework problem 1.2.19, since we are working mod 100, the answer should be greater
than or equal to 0 and less than 100. So an answer such as ─7 should be converted to 93. By
the way, a little thought will cut down enormously on the amount of searching.
Similarly, in 1.5.8 your answer should be a value greater than or equal to 0 and less than 3n+1.
So a negative value should be converted to a value in this range.
3. Your proofs do not have to be overly long, but they should be clear and complete. As an
example, here is a proof of 1.2.16:
Let r be the reduction of N mod m. This means that N=qm+r, where q is some integer and
0<r<|m|. Then N=(─q)(─m)+r, where 0<r<|─m|, so r is also the reduction of N mod ─m.
4. Prof. Stanton, who is teaching the other section of 5248, has posted his homework at
http://www.math.umn.edu/~stanton/5248/5248roster-13.html
You do NOT have to hand in these problems, but his “extra problems” might be a good source
of more practice problems for you.