Homework 1

This assignment is due by the beginning of class on Wednesday, September 3rd. Be sure to review the homework guidelines before getting started.

• Prove that for any $n \in \mathbb{Z}$ and any positive integer $k$, at least one number from the set $\{n,n+1,\cdots, n+k-1\}$ is divisible by $k$. (Note: I made a small change to the problem since the original posting. The old version can also be solved, but this is a little more precise, so it's a better result to carry around in your toolbox.)
• From Strayer, do the following problems:
• 5
• 10(a)
• 11(b),(d)
• 18
• 21(b),(d)
• 23
• 29

It would also be good to get some practice on other problems, even though I won't be collecting them. For this, I'd suggest you take a look at the following problems from Strayer: 1(c), 1(d), 2, 3(b), 12, 25, 30. Any other problems you want to work on are also good practice, so if these problems all seem to easy, try out some others on your own.