# MATH 4460 - Theory of Numbers

Class Information:

Study Guides:

Test solutions

Lecture Notes: These are the notes I'm using to teach the class.   Notes for
specific days for our class will be in the calendar below.

Homework:

 HW 1 Here are the problems and solutions Here's another way to solve problem 10: part 1, part 2 (Note: The pic says problem 9, but that's a typo.) HW 2 Here are the problems and solutions HW 3 Here are the problems and solutions HW 4 Here are the problems and solutions Here is an additional problem: Problem: If n is not a perfect square, then the square root of n is irrational.   Solution: The proof is here. HW 5 Here are the problems and solutions HW 6 Here are the problems and solutions

Schedule and lecture notes:

 week Monday Wednesday 1 1/23- lecture notes 1/25 - lecture notes 2 1/30 - lecture notes 2/1 - lecture notes 3 2/6 - lecture notes 2/8 - lecture notes 4 2/13 - lecture notes 2/15 - lecture notes 5 2/20 - lecture notes 2/22 - lecture notes 6 2/27 - lecture notes 3/1- lecture notes 7 3/6 - no notes for this day 3/8 - lecture notes 8 3/13 - lecture notes 3/15- TEST 1 9 3/20 - lecture notes 3/22 - lecture notes Spring break 3/27 - HOLIDAY 3/29 - HOLIDAY 10 4/3- lecture notes 4/5 - lecture notes 11 4/10 - lecture notes 4/12 - lecture notes 12 4/17 - lecture notes 4/19 - lecture notes 13 4/24 - lecture notes 4/26 - TEST 2 14 5/1 - lecture notes 5/3- lecture notes 15 5/8 - lecture notes 5/10- lecture notes Finals week 5/15 - FINAL EXAM 2:30 pm - 4:30 pm

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: