# Math 580/780I, Elementary Number Theory - Fall 2006

# Nigel Boston

## Contact Information

LeConte 427
Telephone: 777-0439.

E-mail: *boston@math.sc.edu*

Homepage

Office Hours: M 3:30-4:30, T 2-3, W 2:30-3:30, or by appointment.

## Text

Elementary Number Theory, 6th edition (2007), by David Burton.
## Course Overview and Syllabus

Course Information
## Sections

- Main Lecture: TTh 12:30-1:45, LeConte 405.

## Course Schedule

- Aug 24: Overview and background
- Aug 29: Mathematical induction (Chapter 1)
- Aug 31: Binomial theorem (Chapter 1) and some divisibility theory (Chapter 2)
- Sep 5: The division algorithm and some greatest common divisor (Chapter 2)
- Sep 7: Properties of gcd and the Euclidean algorithm (Chapter 2)
- Sep 12: More on Euclidean algorithm and the Diophantine equation ax+by=c (Chapter 2)
- Sep 14: More on Diophantine equations and then properties of primes (Chapter 3)
- Sep 19: More on properties of primes and the sieve of Eratosthenes (Chapter 3)
- Sep 21: The Goldbach conjecture and similar problems (Chapter 3)
- Sep 26: Review for the first test (to cover up to and including 3.1)
- Sep 28: The first test
- Oct 3: Returned test. Started congruences (Chapter 4)
- Oct 5: More on congruences; representing numbers to different bases (Chapter 4)
- Oct 10: Linear congruences and the Chinese Remainder Theorem (Chapter 4)
- Oct 12: Fermat's little theorem (Chapter 5)
- Oct 17: (Absolute) pseudoprimes and Wilson's theorem (Chapter 5)
- Oct 24: Fermat-Kraitchik factorization method (Chapter 5)
- Oct 26: Sum and number of divisors (Chapter 6)
- Oct 31: Euler's phi-function (Chapter 7)
- Nov 2: Review for the second test (to cover up to and including 5.4)
- Nov 9: The second test
- Nov 14: Went over test, more on Euler's phi-function
- Nov 16: Euler's theorem and primitive roots
- Nov 21: Miscellaneous problems
- Nov 28: Miscellaneous problems
- Nov 30: Miscellaneous problems
- Dec 5: Miscellaneous problems
- Dec 7: Review for the final
- Dec 10: Review session for final, 4pm-6pm, LC 405
- Dec 11: Final exam, 2pm-5pm, LC 405

## Homework Assignments

Homework will be set every Thursday and due the following Thursday. You are encouraged to discuss
the exercises with your classmates but the work you hand in should be your own. You will be
expected to read the sections of the book to be covered in advance of class. Homeworks will
consist of about 8 problems, 5 of which will be graded.
- Due Sept 7: 1.1 1(b),(c), 6, 9, 13; 1.2 3(d),(e), 10.
- Due Sept 14: 2.1 7, 10; 2.2 6, 10; 2.3 5, 16, 20(a).
- Due Sept 21: 2.4 2(b), 4(a), 8(a); 2.5 3(a), 5(b), 8(c); 3.1 2, 4.
- No homework due Sep 28: revise for the first test!
- Due Oct 5: 3.1 11, 15; 3.2 3, 5, 12; 3.3 17, 22.
- Due Oct 12: 4.2 3, 4, 8(b)(c), 12; 4.3 3, 10, 27.
- Due Oct 26: 4.4 1(c),(d), 4(a), 11, 12; 5.2 1, 5, 6, 17; 5.3 1, 4.
- Due Nov 2: 5.3 12; 5.4 3,6; 6.1 5(a),7,13,18.
- Due Nov 16: 6.1 19, 20; 7.2 3, 6, 8, 13, 15.
- Due Nov 30: 7.2 21; 7.3 1(c), 5, 9; 8.1 1(b), 3, 10(b).
- Due Dec 7:
3,4,5 from assignment 1; 3 from assignment 2; 2,3 from assignment 3.

## Tests

1st Test
1st Test Solutions
2nd Test
2nd Test Solutions

Final
Final Solutions