 
Summary: 24503 Homework 0.0 Elvis Presley
2. Your first LATEX assignment is to use LATEX to produce a document that replicates this one
as exactly as possible, with just two differences: First, replace the class section number and
name above with your own. Second, make the following letter substitutions so that I know
that you did not just photocopy this document: in Problems 3 and 5, change each m to n;
in Problem 8, change each c to b. Your grade on this assignment will be based on how much
your paper looks like this one.
3. Prove that every integer that is divisible by 6 is even.
Proof. Suppose m Z is divisible by 6. Then there is some k Z such that m = 6k.
Therefore m = 2(3k), and since 3k is also in Z, this means that m is divisible by 2 and
therefore that m is even.
5. Define A = {m Z  m3
 m2
 6m = 0}. Prove that if m A then m = 2, 0, or 3.
Proof. Let A = {m Z  m3
 m2
 6m = 0}. Note that
m3
 m2
 6m = m(m2
