@EE18 Well, Bėzout's identity implies Euclid's lemma, which leads to the Fundamental Theorem of Arithmetic (that every natural number has a unique prime factorisation).

@PM2Ring I think this is what I was thinking about!

I think my book went with Euclidean division algorithm implies FTA, and then got Euclid's Lemma as a corollary

So I See Thorgott's point about order of all this being arbitrary

is any one good at differential equations here?

if $b_t(s)$ satisfies a pde where t is time and s is space

and you add up discrete space slices to obtain a function strictly of time and look at what happens at $t \to \infty$

I wonder if that has a differential equation intepretation

How important is it to know elementary number theory for analysis?

I feel like there are a lot of facts out there in the ether which I don't know

Bezout, Chinese Remainder, Extended Euclid, and I feel like so many more

I figured out how to post 2 questions simultaneously without waiting the 40minutes

I conjecture that it works for $N$ simultaneous questions

implying that I could fill the entire front page

with all my questions

from my calculations there are 100 questions shown at any given time on the front page

Well I guess I will start writing

will I get banned?

I conjecture that 'no' I won't get banned

as it's just a loophole in the system

@EE18 for analysis, none of these matter

OK, will not get sidetracked then

Will I guess leave them for some other study at another time

BTW Thorgott, what do you think the authors have in mind with the below. Exercise 6.3 was just that there are $n \choose k$ $k-element$ subsets of an $n$-element set, and Theorem 8.4 is the binomial theorem. Obviously putting the two together gives me $2^n = \sum_{k=0}^n n \choose k$ but I don't see how that gets me where they're suggesting. I was going to just start by induction but that doesn't seem like what they're suggesting?