Math 312
Assignment #2
Due on Wed 7 October 2015
Solutions should be correct, complete, clear, and neatly presented to get full marks.
It is possible that only a proper subset of the following questions will be marked.
(1) (a) Find the number of element

Math 312
Assignment #1 Answers
Due on 23 September 2015
Solutions should be correct, complete, clear, and neatly presented to get full marks.
Questions 1 -7 are mostly short answer questions. Others require full answers.
(1) Describe the group of symmet

Math 312
Assignment 4
Due on Wed 2 Dec 2015
Only a proper subset of the following questions will be marked
1. Find all ring-homomorphisms from Z Z into Z.
Hint: Chase after elements a satisfying a2 = a. .
2. Find the GCD g of 8 6i and 5 15i in the ring o

Math 312
Assignment #1
Due on 23 September 2015
Solutions should be correct, complete, clear, and neatly presented to get full marks.
It is possible that only a proper subset of the following questions will be marked.
This assignment is mostly a review

On the Gaussian Integers
First a lemma about the integers.
Lemma: If p is a prime number of the form 4n + 1, then there is a solution to the equation x2 = 1
in Zp .
Proof: By Wilsons Theorem (from assignment 3) (p 1)! 1 mod p. (This is true for every
prim

Math 312
Assignment #2
Due on Wed,7 October 2015
Solutions should be correct, complete, clear, and neatly presented to get full marks.
It is possible that only a proper subset of the following questions will be marked.
(1) (a) Find the number of element

Math 312
Assignment #3
Due on Friday 30 October 2015
Except for short-answer questions, answers should be complete, clear, and neatly presented
to get full marks.
Only a proper subset of the following questions will be marked
0. What did you do to celeb