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# MATH619

Resources for MATH619, Spring 2020

### Course information

MATH619 is an introduction to number theory.

• Prerequisites: Math 231 or 237.

• Textbook: I will be lecturing out of the book "Number Theory", by George Andrews.
• Quizzes: There will be one quiz per week, at the end of every Tuesday's class. Every week I will suggest some problems from the book to work on in preparation for the quiz.
• Grading: The final grades will be based around the following rubric: A range is 85-100, B range is 70-84, C range is 60-69, D range is 50-59, and anything below is an F.

### Announcements:

• Week 1: No quiz.
• Week 2:
• Week 3:
• Week 4:
• Week 5:
• Weel 6:
• Week 7:
• Week 8:
• Week 9:
• Week 10:
• Week 11:
• Week 12:
• Week 13:
• Week 14:
• Week 15:

Suggested problems from book: Section 1-1: 1, 5, 7, 10, 12, 18. Section 1-2: 4, 6, 7. Section 2-1: 1 (Hint: represent j to the base k), 6, 7. Section 2-2: 2, 4 (hint: use Corollary 2-1), 8. Section 2-3: 1,5,6,7. Section 2-4: 1,2,3,4,5,7,12. Section 3-1: 1 (Hint: use induction), 2, 3, 8, 9. Section 3-2: 1, 3, 6. Section 3-3: 1. Section 3-4: 1,2,5,8. Section 4-1: 2, 3, 5, 7c, 7d, 7e. Section 4-2: 1, 2, 4. Section 5-1: 1, 3. Section 5-2: 3, 4, 5, 11, 12, 18, 21. Section 5-3: 1d, 2, 4, 5. Section 5-4: 1,3,4,6,7. Section 6-1: 1, 4, 6, 11, 12, 13, 14, 15. Section 6-2: 1, 2, 3, 5, 10, 11, 12, 15. Section 6-3: 1. Section 6-4: 1, 2, 4, 7 (hint: try induction on the number of distinct prime factors of n), 8 (hint: use problem #2 in the same section), 11, 12. Section 7-1: 2, 4, 6, 7. Section 7-2: 4, 8, 9, 11 (hint: phi(p^m) = p^{m-1}(p-1), and g^{phi(m)} = 1 mod m by Euler's theorem. thus, by a result in the section, h divides p^{m-1}(p-1). Now, finish the proof...), 13, 15, 16. Section 8-1: 1,2,3,6,7,8, 15,18. Section 8-2: 1,3. Section 9-1: 1. Section 9-2: 2,3. Section 9-3: 2,4,6 (Hint: perhaps try when m is the square of some small prime). Section 9-4: 1,3,5. Section 10.1: 1. Section 11-1: 1,2. Section 11-2: 1,2,9. Section 12-2: 4, 5, 6. Section 12-3: 1. Section 12-4: 1,2,5. Section 14-5: 1, 2, 5, 6.