MAT 5400 (Elementary Theory of Numbers)
Fall 2007, Section 001, Course Reference Number 10643
Professor Drucker

ASSIGNED EXERCISES

(last updated November 30, 2007)

Text: James K. Strayer, Elementary Number Theory, Waveland Press, Inc., 2002.

ADVICE: Do these assignments as we come to them. Solve extra exercises when you have trouble with a topic. Exercises marked with a star (asterisk) should be turned in for grading. The solutions to such exercises should be entirely your own, though you are allowed to come to me for help if you get stuck. You should not be doing “research” to find solutions to exercises in other texts, and you should not be solving starred exercises with other students or with the help of tutors. The purpose of the starred exercises is to develop your problem-solving skills. Exercises marked with a plus sign are optional. If you solve them, turn them in for grading. As with starred exercises, solutions to optional exercises should be entirely your own. When only part of an exercise is assigned, please read and think about the rest of it. Note that hints or answers to many exercises 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 find ways to check your work other than looking at the answers.
Chapter 1. Divisibility and Factorization
1.1 #1–7, 10* [use induction in parts a and b], 11, 12, 14, 15bd
1.2 #16, 17, 18b, 19–22, 23+, 25*, 29, 30+
1.3 #32, 33, 35, 36, 37*, 38*, 40+, 41+, 42a*, 43ab, 44*, 51, 53*
1.4 #54, 55, 56, 57a, 58b
1.5 #59–61, 63, 65–67, 70b, 72, 76. Read #81.
Chapter 2. Congruences
2.1 #1–6, 8, 13, 21, 22*
2.2 #28, 29, 30ac, 32
2.3 #33, 34, 36*, 38+, 39, 41 (read #40)
2.4 #42–45, 47, 48
2.5 #51, 52, 53*, 54, 57–59, 61
2.6 #66, 68–71, 73*, 75*
Chapter 3. Arithmetic Functions
3.1 #3–8
3.2 #9, 10, 12, 13abcd*ef*, 16, 17, 20–23, 25*
3.3 # 29–32, 35, 37, 39
3.4 #41–45, 47, 49–51
3.5 #53, 54b, 56+
3.6 #63, 66, 67*, 68*, 69+
Chapter 4. Quadratic Residues
4.1 #1ac, 2, 3, 5, 6*, 7a, 10ab*cd*, 11+
4.2 #12–15, 16*, 17, 18*, 20+, 24ab, 26*
4.3 #28–30, 32*, 33, 35, 37, 38*
    CORRECTION: In #38f, the p in the exponent should be an n.
       In #38g, the b in the exponent should be an n.
Chapter 5. Primitive Roots
5.1 #1–4, 5+, 7, 9*
5.2 #10, 11, 12*, 13, 14*, 15, 16a*b, 18, 19
5.3 #23–25, 26*
5.4 #29–33, 34*, 35* [Hint: For #34 and 35, use #12a.]
Chapter 6. Diophantine Equations
6.1 #1–6
6.2 #11, 12
6.3 #13, 14a*b*c*e*
6.4 #
6.5 #
Chapter 7. Continued Fractions
7.1 #1, 2, 3+, 4*, 5
Chapter 8. A Few Applications
8.1 #
8.2 #
8.3 #13bcf, 14a*b*
Appendix A. Mathematical Induction
#1, 2a, 2b+
Appendix B. Equivalence Relations
#1+

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