Quizzes: I somehow completely forgot to give the badges quiz on Friday, for which I apologize (I really try to avoid surprises). We will take it on Monday instead. That will also push the proof quiz back to Wednesday next week.

Today we did a warmup direct proof and I left you with two proofs to write at home:

Let a,b,c be integers. Then .

If a,b,c are integers such that a|b and a|c then a|(b+c) and a|(b-c).

In class we used the fact that the equation xy=1 has only two solutions in the integers, namely x=y=1 and x=y=-1. Can you prove this? Try contradiction!

Review the proofs by contradiction from class and also the first Proposition in Chapter 6 of Hammack (first page of the chapter), which is an example. Pay careful attention to the negation of the theorem, i.e. the supposition you make for contradiction.

With your remaining time, try a few at home: Chapter 6 exercises 1,2,6,7,8,9 as time allows.