245-03 Homework 0.0 Elvis Presley 2. Your first LATEX assignment is to use LATEX to produce a document that replicates this one Summary: 245-03 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 Collections: Mathematics