MATH 4460 - Theory of Numbers

Class Information:

  • The syllabus is here

Test solutions:

  • Test 1 solutions are here.
  • Test 2 solutions are here.   Here's another way to do problem 5 that a student proved on their test.


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!

My Lecture notes:

  • 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.

Student lecture notes from Spring 2018:
(Thank you Cynthia for all the notes, except for week 13 part 2 which was provided by Amy.)