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
and any positive integer 
, at least one number from the set 
is divisible by . (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.
page_revision: 14, last_edited: 1225306964|%e %b %Y, %H:%M %Z (%O ago)
Heyy! Having some trouble with proving the first part. I broke it down into three different cases and proved that it held true for all the cases. My cases were as follows:
1) n > k
2) n < k
3) n = k
Anyone else go about this problem differently??
Also, on the homework, I thought it was very helpful on problem 11 to prove that any even plus any odd is equal to an odd number. After proving that, I used that claim to prove the other parts.
Well anyway, if you could provide any input on the first problem, that would be very helpful. Thanks!
~Alex
Try using the division algorithm on n, with d=k. Then you just need to figure out how to show that for each possible r, you can find an element in the set that would be divisible by k.