# MATH 4460 - Theory of Numbers

Class Information:

Homework:

Schedule and lecture notes:

 week Monday Wednesday 1 1/25- lecture notes 1/27 - lecture notes 2 2/01 - lecture notes 2/03 - lecture notes 3 2/08 - lecture notes 2/10 - lecture notes (General case proof of theorem in class if interested) 4 2/15 - lecture notes 2/17 - lecture notes 5 2/22 - lecture notes 2/24 - lecture notes 6 3/01 - lecture notes 3/03- lecture notes 7 3/08 - lecture notes 3/10 - lecture notes 8 3/15 - lecture notes 3/17 -  TEST 1 covers  HW 1 and HW 2 9 3/22 - lecture notes 3/24 - lecture notes Spring break 3/29 - HOLIDAY 3/31 - HOLIDAY 10 4/5- lecture notes 4/7 - lecture notes 11 4/12 - lecture notes 4/14 - lecture notes 12 4/19 - lecture notes 4/21 - lecture notes 13 4/26 - lecture notes 4/28 - TEST 2 covers HW 3, 4, 5 14 5/3 - lecture notes 5/5 - lecture notes 15 5/10 - lecture notes 5/12- lecture notes Finals week 5/17 -  FINAL EXAM 2:30pm - 4:30pm 5/19 -

My notes from my notebook (if you want to look ahead):

• Topic 0 - Assumptions about the integers
• Topic 1 - Division and Primes
Note: Pages 12--15 are a handout that I will give you.
• Topic 2 - GCD
(Note: There is no page 5 in the GCD notes above, that's a numbering mistake in the page numbering)
• Topic 3 - Linear Diophantine Equations
• Topic 4 - The Fundamental Theorem of Arithmetic
• Topic 5 - Construction of Z_n and the properties of Z_n
• Topic 6 - Pythagorean Triples
• Topic 7 - The Multiplicative Structure of Z_n
• Topic 8 - Gaussian Integers
• Topic 9 - Fermat's Last Equation for n = 4 - This will be a handout that I will give you.

Computer Programs:

• Here is a program to find z and w in the Gaussian integers where N(z) divides N(w) but z does not divide w.   It finds non-trivial cases, ie ones where N(z) is not 1 and not equal to N(w).   I only ran it with 1 < N(w) <= 10.
• Here is a program that finds all the divisors of a Gaussian integer and also tests if a Gaussian integer is prime.   It does what we do in the HW but way faster.   Note that z = 100 has 180 divisors!

For Fun: