[SOLVED] Abstract Algebra: Congruence and The Division Algorithm 2
Now this problem makes me feel even stupider than the last one. But then again, I was always bad at choosing examples. Again, hints are what I want, but it may be hard to do here, since this is a give-an-example question. So if you give an example, tell me your thought process and I'll try to come up with one on my own.
Disprove with a counter-example: If is a positive integer and , then there is an integer such that
Things that may come in handy:
The following statments are equivalent:
What I've Tried:
All kinds of foolishness. On my latest attempt:
...wait! does work?!
That just came to me when I was typng out my "method" (I'll let you see it if you're interested, so you can comment on whether or not my reasoning was sound).
Still check the example, I didn't sleep last night, so it might be that this is obviously wrong, but I'm too tired to tell.
Thanks guys (and gals -- dedicated to JaneBennet... again)