MATH 346
Number Theory, Spring 2012

Lectures:

MWF 3:00-3:50, 191 Anstett Hall

Office hours:

Tuesday 12-1, or by appointment

My office:

207 Deady, phone 3465635, e-mail apolish@uoregon.edu

Textbook:

Elementary Number Theory by Charles Vanden Eynden
2nd edition,

Homework:

Assignments will be posted on this web page. Homework will be collected on Fridays, at the beginning of class (with the exception of the first assignment that will be collected on Wednesday, April 11). Late homework will not be accepted. You are encouraged to collaborate on homeworks, however, writing up the solutions should be an individual work. Not all of the assigned homework problems will be graded. The lowest homework score will be dropped.

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Midterm: will be held in class on May 4.

Final: June 12 at 3:15pm

Grading:

homework 35%
midterm 25%
final 40%

Schedule:

week 1 (April 2-April 6) Divisibility properties, Division with remainder, Euclidean algorithm (sections 1.1, 1.1, 1.2)

Assignment #1 (due April 11)

section 1.1: problems 4,6,8,18,24,26
section 1.2: problems 2,4,12,14,16,18,20,22,26
section 1.3: problems 1,7,10,11,18

week 2 (April 9-13) Congruences (sections 1.4, 1.5, 4.1)

Assignment #2 (due April 20)

section 1.4: problems 4, 10, 14, 22, 36, 37, 38
section 1.5: problems 10, 16, 28, 32, 42, 46
section 4.1: problems 4, 6, 14, 16, 44, 48

week 3 (April 16-20) Induction, Prime factorization (sections 1.6, 2.1, 2.2, 2.4)

Assignment #3 (due April 27)

section 1.6: problems 21, 29, 32, 41, 44, 60
section 2.1: problems 25, 26
section 2.2: problems 22, 24, 25
section 2.4: problems 8, 32, 37, 38

week 4 (April 23-27) Prime factorization, Chinese remainder theorem, Reduced residue systems (section 4.2)

Assignment #4 (due May 4)

section 2.4: problems 43, 49
section 4.2: problems 4, 8, 16, 21, 25, 32, 38, 40, 44

Review problems for the midterm exam (covering sections 1.1-1.6, 2.1, 2.2, 2.4, 4.1, 4.2): 1.1.36, 1.2.36, 1.3.16, 1.3.28, 1.4.23, 1.4.35, 1.5.24, 1.5.36, 1.5.47, 1.6.35, 1.6.39, 1.6.48, 2.3.39, 2.4.47, 2.4.51, 4.1.17, 4.1.29, 4.1.46, 4.1.47, 4.2.11, 4.2.42, 4.2.48, 4.2.49.

week 5 (April 30-May 4) Theorems of Fermat and Euler (section 4.3)

Assignment #5 (due May 14)

section 4.2: problem 51 (Hint: first, solve the following problem. Given a pair of distinct prime numbers p and q prove that there exists an integer n divisible by p^2 such that n+1 is divisible by q^2.)
section 4.3: problems 10, 16, 20, 24, 28, 34, 39

week 6 (May 7-May 11) Multiplicative orders, Euler phi function, RSA method (sections 4.3, 3.5, 4.5)

Assignment #6 (due May 18)

section 4.3: problems 21, 25, 26, 36, 37, 49
section 3.5: problems 42, 44, 45, 46
section 4.5: problems 24, 28

week 7 (May 14-May 18) Quadratic residues (sections 5.3, 5.4)

Assignment #7 (due May 25)

section 5.3: problems 4, 6, 14, 26, 36, 43 (with proof).
section 5.4: problems 2, 4, 10, 14, 30, 37

Review problems on Pythagorean triples and sums of two squares:

7.1.10, 7.1.31, 7.1.32, 7.1.35, 7.2.8, 7.2.12, 7.2.20.

The final exam covers the material we studied except for Sections 7.3 and 7.4.

Solutions to selected homework problems: set 1, set 2, set 3, sections 4.2-4.3, sections 4.5, 5.3-5.4.

MATH 346 Number Theory, Spring 2012