## 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 $n$.