# MATH 4460 - Theory of Numbers

Class Information:

Past Lecture Notes:

Homework:

 HW 1 Here are the problems and solutions Here's another way to solve problem 10: part 1, part 2 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 1/24- lecture notes 1/26 - lecture notes 2 1/31 - lecture notes 2/2 - lecture notes 3 2/7 - lecture notes 2/9 - lecture notes                  +          proof of general       theorem from class 4 2/14 - lecture notes 2/16 - lecture notes 5 2/21 - lecture notes 2/23 - lecture notes 6 2/28 - lecture notes 3/2- lecture notes 7 3/7 - lecture notes 3/9 - TEST 1 8 3/14 - lecture notes 3/16 - lecture notes 9 3/21 - lecture notes 3/23 - lecture notes Spring break 3/29 - HOLIDAY 3/31 - HOLIDAY 10 4/4- lecture notes 4/6 - lecture notes 11 4/11 - lecture notes 4/13 - lecture notes 12 4/18 - lecture notes 4/20 - lecture notes 13 4/25 - TEST 2 4/27 - lecture notes 14 5/2 - lecture notes 5/4 - lecture notes 15 5/9 - lecture notes 5/11- lecture notes Finals week 5/16 - final 2:30 - 4:30 5/18 -

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: