MAT 5400 (Elementary Theory of Numbers)
Fall 2009, Section 001, Course Reference Number 10453
Professor Drucker

ASSIGNMENTS

Text: Underwood Dudley, Elementary Number Theory, Second Edition, Dover, ISBN 048646931X.

ADVICE: In Dudley’s text, “exercises” are easy questions scattered throughout the text that you should solve to check your understanding as you read the book. If you have trouble with any of them, ask about them in class. “Problems” are somewhat more challenging. The assignments consist of problems.
     Do these assignments as we come to them. Solve extra problems when you have trouble with a topic. It is permissible to discuss problems with classmates, provided you write your own solutions in your own words and your own notation. (Don’t copy classmates’ solutions.) You are also allowed to come to me for help if you get stuck. You should not be doing “research” to find solutions in other texts, partly because other texts obtain their results in a different logical order, but mostly because the purpose of the assignments is to try out your own problem-solving skills and get feedback from me. For the same reason you should not solve problems with the help of tutors, other professors, or students not in our class.
     Problems are listed by section. For example, “§1” means “Section 1”. “AP§1” refers to the Additional Problems for Section 1 on page 183.
     When only part of a problem is assigned, please read and think about the rest of it. In fact, it would be a good idea to at least read all the problems, partly to notice some additional facts, but also because some of them may pique your interest. Note that hints and/or answers to many problems are given at the back of the text. Don’t look at the answers until you’ve completed the exercises. Working “toward an answer” leads to bad habits. Your goal should be to develop confidence in your problem-solving skills and to find ways to check your work other than looking at the answers.

Assigned problems

§1 #1, 2, 4–10, 12–15;   AP§1 #4, 7, 8a.

Appendix A #1–6, 11, 14.   After solving #11 by use of induction, try to do it without using induction.

§2 #1–10, 14, 15;   AP§2 #3. If your book says “2^n–1” in #14, change it to read “ 2ⁿ–1”.

§3 #1–10. [Note: The answer to #3 (on page 231) may be wrong in some copies of the text.]

§4 #1, 3–5, 7–9, 11–14, 16–18;   AP§4 #1, 10.

§5 #1, 3, 5, 6, 11, 16, 18, 19;   AP§5 #5.

§6 #1, 3, 4, 7, 9, 10–12, 16, 19, 20;   AP§6 #1, 5, 6.

§7 #1, 3, 5–9, 11–14, 20;   AP§7 #1, 4.

§8 #3, 5, 7, 9, 10.

§9 #1, 3, 5, 7, 10 (the sums are over primes p≤x), 15, 18, 19.

§10 #3, 5, 7, 9, 14, 15, 17;   AP§10 $1, 3, 5, 13.

§13 #1–13 odd, 17, 19;   AP§13 #1, 3, 5.