The Division Algorithm
OK. I'm clearly in over my head. I bought this intro to number theory, and I figured I'd start working at it now while I'm still taking the lower level undergrad stuff so that when I get to this subject, I've had a really good introduction to it.
Having said that, I want you guys to understand that I can MAYBE do 1 of the problems given in each exercise set after the sections, but I don't want to skip the others, I want to see them worked out - that way I can get a really good grip on what's going on. So, without further adieu, can someone help me with the following?
Let , so that
where the and are all rational numbers. If , show that the degree of
is less than .
I don't even know where to begin. I am sophisticated enough, however, to understand if a proof is valid or not due to my introductory course in logic. Thank you all for looking at this post.
I see that
Notice the first term of the expression and first term inside the brackets now cancel giving the order of the greatest term being
Thus the leading term from above cancels out the leading term of .
It's difficult to understand why I didn't see that. I mean, I can mutiply and subtract. I guess it's just that the rest of the problems in this book are so tough that I naturally expected this one to be as well. Thanks.
Originally Posted by chiph588@