## Monthly Archives: September 2008

### Proof of Bezout’s Lemma

Dear Prof Kim

I just have a question referring the notation in your proof Bezout’s Lemma in the notes. My question arises about the first line where you write out the sequence given by Euclid’s algorithm. The final term (which is equal to d) has a subscript n, should this be a subscript i?

I ask because it would seem to make more sense to me this way when doing induction on i. Or is it unimportant? Or have I misunderstood?

Reply: There is no misprint. The intention is that $n$ is whatever the index is when we have reached the hcf $d$. And then, the induction is done on $i$ as $i$ ranges from 1 to $n$.

### New Year

As another academic year begins, I urge students in my LInear Algebra class and my Algebraic Number Theory class to make full use of this blog. You might start by going to the very first posts that were around late October of the previous year. As you move forward, you will get a sense of the kind of things that were discussed here, and how you might yourself best take advantage of this resource. Also useful might be to look at the posts that go from March to May of 2008. There, you will find material that deals with many different aspects of the examinations. You might find that even vague questions you have are already answered there. Looking at them at the very beginning could be a substantial aid to you as you study through the year.

The search function can be used for specific topics. For example, typing ‘Jordan’ will bring up all kinds of articles on the Jordan canonical form. My hope is that browsing through the previous discourse will help you focus your attention on the important issues, as well provide specific help with mathematical questions.