Talk:Fermat's Two Squares Theorem/Uniqueness Lemma

Fri, 15 Sep 2023 19:55:13 User:Usagiop added a 3rd proof derived from the 1st one. Must choose one of both!

Yes, as I asked there, I cannot see how you derive:

$\dfrac{d^2}{b^2}=\dfrac{c^2+d^2}{a^2+b^2}$

Can you please explain this, first?

Sure, we can discuss about deleting Proof 3, after you improved your Proof 1. --Usagiop (talk) 20:09, 15 September 2023 (UTC)

I don't see why we need both Proof 1 and Proof 3 considering they are the same. --prime mover (talk) 20:21, 15 September 2023 (UTC)

Yes, if they are the same, then delete Proof 3. It was not clear how User:Fabo34 wanted to finish his last argument, which I am still looking forward to know. By the way, I changed my last argument, because User:Fabo34 said that was the same as his idea. Now, it should be different. --Usagiop (talk) 20:38, 15 September 2023 (UTC)

i done the tidying an justification linx, left an explain template --prime mover (talk) 20:50, 15 September 2023 (UTC)

Thanks, I also changed the first part of my proof. --Usagiop (talk) 21:18, 15 September 2023 (UTC)

it is a basic numerical fact when writting if $\dfrac{u}{v}=\dfrac{r}{s}$ then $\dfrac{u}{v}=\dfrac{r}{s}=\dfrac{u+r}{v+s}$. It is always true. I am not sure it's worth detailing this. But If you think it is, then feel free to add that. I am new on this site and I don't know the required level of precision. fabo34 16 Sep 2023 06:41:25 (UTC)

Indeed? Your mission, Jim, should you choose to accept it, is to prove it. This tape will self-destruct in 5 seconds. Good luck, Jim. --prime mover (talk) 08:07, 16 September 2023 (UTC)

Okay I've finished the work.

The whole point is that every statement made has to be linked back to a page which proves that statement. This is a hard and fast rule of $\mathsf{Pr} \infty \mathsf{fWiki}$.

We encourage contributors to either study the house rules to get an idea of how the site works, and how pages are presented, or to use existing pages as examples of how pages are to be presented.

This also applies to source code style, which can appear to be an imposition to those people who already have a feel for $\LaTeX$, because their style of presentation is probably non-compliant with $\mathsf{Pr} \infty \mathsf{fWiki}$ style. --prime mover (talk) 09:22, 16 September 2023 (UTC)

"This is a hard and fast rule of Pr∞fWiki" : yes, it is! Seems you did it great and found a link. Maybe $\dfrac{u+r}{v+s}=\dfrac{u}{v}\times\dfrac{1+r/u}{1+s/v}=\dfrac{r}{s}\times\dfrac{1+u/r}{1+v/s} \Rightarrow \dfrac{u}{v}=\dfrac{r}{s}=\dfrac{u+r}{v+s}$ is just speaking enough, and may not deserve a complete page? fabo34 16 Sep 2023 12:02:13

I'll let you fill in the details. Dunno why you had to go and change the variable names, I had to change the damn things back again. You're going to need to explain how that final step happens, because it is far from obvious. --prime mover (talk) 17:06, 16 September 2023 (UTC)