Homework 8

This assignment is due to my office by 11am on Wednesday, October 22nd. Be sure to review the homework guidelines before getting started.

• Suppose that p is an odd prime and that $p \nmid a$. If we let $a^*$ denote the multiplicative inverse of a modulo p, prove that $\left(\frac{a}{p}\right) = \left(\frac{a^*}{p}\right)$.
• From Chapter 4 of Strayer, do the following problems
• 17
• 24
• 26
• 28(bdf)
• 33
• 34
• 36(d)
• From Chapter 5 of Strayer, do the following problems
• 1(d)
• 3(a)
• Answer the following question in a short paragraph. You answer should be well-thought out, and your writing should be clear and concise.

We spend a lot of time in this course discussing proofs, and you spend a good bit of your time on homework assignments writing proofs. Is there a non-mathematical benefit to all this emphasis on proof? If so, what skills do you gain from learning and practicing proofs that you can apply outside the math classroom? If not, how could we change the focus of class discussions and homework assignments to be more "real-world oriented"?

It would also be good to get some practice on other problems, even though I won't be collecting them. There are loads of these problems in your book and elsewhere, so give some a shot.