MATH 4460 - Theory of Numbers

Class Information:

• Syllabus

Study Guides:

• Here is the test 1 study guide
  Here are some practice tests for test 1.
   
• Here is the test 2 study guide.
  Test 2 practice tests coming soon......

Test solutions

• Test solutions will go here....

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.   

• Topic 1 - Division and primes
• Topic 2 - GCD
• Topic 3 - Fundamental theorem of arithmetic
• Topic 4 - Z_n, the integers modulo n
• Topic 4.5 - Application to Pythagorean triples
• Topic 5 - Multiplicative structure of Z_n
• Topic 6 - Gaussian integers

Homework:

Schedule and lecture notes:

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:

• Sums of three cubes is an unsolved problem.   Computation results on this problem.